0=-5x^2+24x-20

Solution for 0=-5x^2+24x-20 equation:

0=-5x^2+24x-20

We move all terms to the left:

0-(-5x^2+24x-20)=0

We add all the numbers together, and all the variables

-(-5x^2+24x-20)=0

We get rid of parentheses

5x^2-24x+20=0

a = 5; b = -24; c = +20;
Δ = b2-4ac
Δ = -242-4·5·20
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{11}}{2*5}=\frac{24-4\sqrt{11}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{11}}{2*5}=\frac{24+4\sqrt{11}}{10}
$