0=9x^2-100x-20

Solution for 0=9x^2-100x-20 equation:

0=9x^2-100x-20

We move all terms to the left:

0-(9x^2-100x-20)=0

We add all the numbers together, and all the variables

-(9x^2-100x-20)=0

We get rid of parentheses

-9x^2+100x+20=0

a = -9; b = 100; c = +20;
Δ = b2-4ac
Δ = 1002-4·(-9)·20
Δ = 10720
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:

$\sqrt{\Delta}=\sqrt{10720}=\sqrt{16*670}=\sqrt{16}*\sqrt{670}=4\sqrt{670}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{670}}{2*-9}=\frac{-100-4\sqrt{670}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{670}}{2*-9}=\frac{-100+4\sqrt{670}}{-18}
$