Y=x^2-180x-30

Solution for Y=x^2-180x-30 equation:

=Y^2-180Y-30

We move all terms to the left:

-(Y^2-180Y-30)=0

We get rid of parentheses

-Y^2+180Y+30=0

We add all the numbers together, and all the variables

-1Y^2+180Y+30=0

a = -1; b = 180; c = +30;
Δ = b2-4ac
Δ = 1802-4·(-1)·30
Δ = 32520
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:

$\sqrt{\Delta}=\sqrt{32520}=\sqrt{4*8130}=\sqrt{4}*\sqrt{8130}=2\sqrt{8130}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8130}}{2*-1}=\frac{-180-2\sqrt{8130}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8130}}{2*-1}=\frac{-180+2\sqrt{8130}}{-2}
$