4x(x-9)=-8

Solution for 4x(x-9)=-8 equation:

4x(x-9)=-8

We move all terms to the left:

4x(x-9)-(-8)=0

We add all the numbers together, and all the variables

4x(x-9)+8=0

We multiply parentheses

4x^2-36x+8=0

a = 4; b = -36; c = +8;
Δ = b2-4ac
Δ = -362-4·4·8
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{73}}{2*4}=\frac{36-4\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{73}}{2*4}=\frac{36+4\sqrt{73}}{8}
$