4x(x-9)+7=32

Solution for 4x(x-9)+7=32 equation:

4x(x-9)+7=32

We move all terms to the left:

4x(x-9)+7-(32)=0

We add all the numbers together, and all the variables

4x(x-9)-25=0

We multiply parentheses

4x^2-36x-25=0

a = 4; b = -36; c = -25;
Δ = b2-4ac
Δ = -362-4·4·(-25)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{106}}{2*4}=\frac{36-4\sqrt{106}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{106}}{2*4}=\frac{36+4\sqrt{106}}{8}
$