Solution of a Quadratic Equation

Solve: $\sqrt{6+\sqrt{6+\sqrt{6+.......}}}$

Solve and check the answer $3x^2+10x+8=0$

The ratio of the length and breadth of a rectangular garden is $3 : 2$. If the area of the garden is $600$ square metres, find its length and breadth.

$I. 12x^2-8x-7=0$

$II. 10y^2+23y+12=0$

The roots of the Quadratic equation $x^2+2x-3=0$ are:

To save fuel, to avoid air pollution and for good health two persons $A$ and $B$ ride bicycle for a distance of $12 \mathrm{km}$ to reach their office. As the cycling speed of $B$ is $2 \mathrm{km}/\mathrm{h}$ more than that of $A, B$ takes $30$ minutes less than that of $A$ to reach the office. Find the time taken by $A$ to reach the office in hours.

A dealer sells a toy for $₹24$ and gains as much percent as the cost price of the toy. Find the cost price of the toy in rupees.

Write Shridhar Acharya's formula to find roots of quadratic equation $a{x}^2+bx+c=0$.

Divide $16$ into two parts, such that $2$ times the square of larger part is $164$ more than the square of smaller part.

Find the roots of the quadratic equation, if they exist, using the quadratic formula of Shridhar Acharya.
$x^2+4x+5=0$

Find the roots of the quadratic equation, if they exist, using the quadratic formula of Shridhar Acharya.
$x+\frac{1}{x}=3, x\ne 0$

Find the roots of the quadratic equation, if they exist, using the quadratic formula of Shridhar Acharya.
$9x^2+7x-2=0$

Solve the quadratic equation by the method of perfect the square.
$4x^2+4bx-\left(a^2-b^2\right)=0$

Solve the quadratic equation by the method of perfect the square.
$2x^2+x-4=0$

Solve the quadratic equation by the method of perfect the square.
$4x^2+4\sqrt{3}x+3=0$

Solve the quadratic equation by the method of perfect the square.
$5x^2-6x-2=0$

Solve the quadratic equation by the method of perfect the square.
$3x^2-5x+2=0$

Solve the equation by factorisation method.
$ab{x}^2+\left(b^2-ac\right)x-bc=0$

Solve the equation by factorisation method.

$4x^2-4a^{2}x+\left(a^4-b^4\right)=0$

Solve the equation by factorisation method.
$\frac{x+3}{x+2}=\frac{3x-7}{2x-3}$