Y=x^2-50x-50

Solution for Y=x^2-50x-50 equation:

=Y^2-50Y-50

We move all terms to the left:

-(Y^2-50Y-50)=0

We get rid of parentheses

-Y^2+50Y+50=0

We add all the numbers together, and all the variables

-1Y^2+50Y+50=0

a = -1; b = 50; c = +50;
Δ = b2-4ac
Δ = 502-4·(-1)·50
Δ = 2700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-30\sqrt{3}}{2*-1}=\frac{-50-30\sqrt{3}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+30\sqrt{3}}{2*-1}=\frac{-50+30\sqrt{3}}{-2}
$