5x(32-6x)=12

Solution for 5x(32-6x)=12 equation:

5x(32-6x)=12

We move all terms to the left:

5x(32-6x)-(12)=0

We add all the numbers together, and all the variables

5x(-6x+32)-12=0

We multiply parentheses

-30x^2+160x-12=0

a = -30; b = 160; c = -12;
Δ = b2-4ac
Δ = 1602-4·(-30)·(-12)
Δ = 24160
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:

$\sqrt{\Delta}=\sqrt{24160}=\sqrt{16*1510}=\sqrt{16}*\sqrt{1510}=4\sqrt{1510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-4\sqrt{1510}}{2*-30}=\frac{-160-4\sqrt{1510}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+4\sqrt{1510}}{2*-30}=\frac{-160+4\sqrt{1510}}{-60}
$