4x(32-x)=156

Solution for 4x(32-x)=156 equation:

4x(32-x)=156

We move all terms to the left:

4x(32-x)-(156)=0

We add all the numbers together, and all the variables

4x(-1x+32)-156=0

We multiply parentheses

-4x^2+128x-156=0

a = -4; b = 128; c = -156;
Δ = b2-4ac
Δ = 1282-4·(-4)·(-156)
Δ = 13888
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:

$\sqrt{\Delta}=\sqrt{13888}=\sqrt{64*217}=\sqrt{64}*\sqrt{217}=8\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-8\sqrt{217}}{2*-4}=\frac{-128-8\sqrt{217}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+8\sqrt{217}}{2*-4}=\frac{-128+8\sqrt{217}}{-8}
$