5*(29.6-x)x=40

Solution for 5*(29.6-x)x=40 equation:

5*(29.6-x)x=40

We move all terms to the left:

5*(29.6-x)x-(40)=0

We add all the numbers together, and all the variables

5*(-1x+29.6)x-40=0

We multiply parentheses

-5x^2+148x-40=0

a = -5; b = 148; c = -40;
Δ = b2-4ac
Δ = 1482-4·(-5)·(-40)
Δ = 21104
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:

$\sqrt{\Delta}=\sqrt{21104}=\sqrt{16*1319}=\sqrt{16}*\sqrt{1319}=4\sqrt{1319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(148)-4\sqrt{1319}}{2*-5}=\frac{-148-4\sqrt{1319}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(148)+4\sqrt{1319}}{2*-5}=\frac{-148+4\sqrt{1319}}{-10}
$