0=50x^2+100x-80

Solution for 0=50x^2+100x-80 equation:

0=50x^2+100x-80

We move all terms to the left:

0-(50x^2+100x-80)=0

We add all the numbers together, and all the variables

-(50x^2+100x-80)=0

We get rid of parentheses

-50x^2-100x+80=0

a = -50; b = -100; c = +80;
Δ = b2-4ac
Δ = -1002-4·(-50)·80
Δ = 26000
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:

$\sqrt{\Delta}=\sqrt{26000}=\sqrt{400*65}=\sqrt{400}*\sqrt{65}=20\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{65}}{2*-50}=\frac{100-20\sqrt{65}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{65}}{2*-50}=\frac{100+20\sqrt{65}}{-100}
$