4x(x+9)=76

Solution for 4x(x+9)=76 equation:

4x(x+9)=76

We move all terms to the left:

4x(x+9)-(76)=0

We multiply parentheses

4x^2+36x-76=0

a = 4; b = 36; c = -76;
Δ = b2-4ac
Δ = 362-4·4·(-76)
Δ = 2512
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2512}=\sqrt{16*157}=\sqrt{16}*\sqrt{157}=4\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{157}}{2*4}=\frac{-36-4\sqrt{157}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{157}}{2*4}=\frac{-36+4\sqrt{157}}{8}
$