Y=x^2-21x-130

Solution for Y=x^2-21x-130 equation:

=Y^2-21Y-130

We move all terms to the left:

-(Y^2-21Y-130)=0

We get rid of parentheses

-Y^2+21Y+130=0

We add all the numbers together, and all the variables

-1Y^2+21Y+130=0

a = -1; b = 21; c = +130;
Δ = b2-4ac
Δ = 212-4·(-1)·130
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-31}{2*-1}=\frac{-52}{-2}
=+26
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+31}{2*-1}=\frac{10}{-2}
=-5
$