0=50x^2+100x-110

Solution for 0=50x^2+100x-110 equation:

0=50x^2+100x-110

We move all terms to the left:

0-(50x^2+100x-110)=0

We add all the numbers together, and all the variables

-(50x^2+100x-110)=0

We get rid of parentheses

-50x^2-100x+110=0

a = -50; b = -100; c = +110;
Δ = b2-4ac
Δ = -1002-4·(-50)·110
Δ = 32000
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:

$\sqrt{\Delta}=\sqrt{32000}=\sqrt{6400*5}=\sqrt{6400}*\sqrt{5}=80\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-80\sqrt{5}}{2*-50}=\frac{100-80\sqrt{5}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+80\sqrt{5}}{2*-50}=\frac{100+80\sqrt{5}}{-100}
$