4x(8-x)=12

Solution for 4x(8-x)=12 equation:

4x(8-x)=12

We move all terms to the left:

4x(8-x)-(12)=0

We add all the numbers together, and all the variables

4x(-1x+8)-12=0

We multiply parentheses

-4x^2+32x-12=0

a = -4; b = 32; c = -12;
Δ = b2-4ac
Δ = 322-4·(-4)·(-12)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{13}}{2*-4}=\frac{-32-8\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{13}}{2*-4}=\frac{-32+8\sqrt{13}}{-8}
$