5*(29.6-x)x=12

Solution for 5*(29.6-x)x=12 equation:

5*(29.6-x)x=12

We move all terms to the left:

5*(29.6-x)x-(12)=0

We add all the numbers together, and all the variables

5*(-1x+29.6)x-12=0

We multiply parentheses

-5x^2+148x-12=0

a = -5; b = 148; c = -12;
Δ = b2-4ac
Δ = 1482-4·(-5)·(-12)
Δ = 21664
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:

$\sqrt{\Delta}=\sqrt{21664}=\sqrt{16*1354}=\sqrt{16}*\sqrt{1354}=4\sqrt{1354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(148)-4\sqrt{1354}}{2*-5}=\frac{-148-4\sqrt{1354}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(148)+4\sqrt{1354}}{2*-5}=\frac{-148+4\sqrt{1354}}{-10}
$