0=-20x^2+90x-68

Solution for 0=-20x^2+90x-68 equation:

0=-20x^2+90x-68

We move all terms to the left:

0-(-20x^2+90x-68)=0

We add all the numbers together, and all the variables

-(-20x^2+90x-68)=0

We get rid of parentheses

20x^2-90x+68=0

a = 20; b = -90; c = +68;
Δ = b2-4ac
Δ = -902-4·20·68
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{665}}{2*20}=\frac{90-2\sqrt{665}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{665}}{2*20}=\frac{90+2\sqrt{665}}{40}
$