5x(24-x)=162

Solution for 5x(24-x)=162 equation:

5x(24-x)=162

We move all terms to the left:

5x(24-x)-(162)=0

We add all the numbers together, and all the variables

5x(-1x+24)-162=0

We multiply parentheses

-5x^2+120x-162=0

a = -5; b = 120; c = -162;
Δ = b2-4ac
Δ = 1202-4·(-5)·(-162)
Δ = 11160
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:

$\sqrt{\Delta}=\sqrt{11160}=\sqrt{36*310}=\sqrt{36}*\sqrt{310}=6\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-6\sqrt{310}}{2*-5}=\frac{-120-6\sqrt{310}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+6\sqrt{310}}{2*-5}=\frac{-120+6\sqrt{310}}{-10}
$