Y=x2-13x-12

Solution for Y=x2-13x-12 equation:

=Y2-13Y-12

We move all terms to the left:

-(Y2-13Y-12)=0

We add all the numbers together, and all the variables

-(+Y^2-13Y-12)=0

We get rid of parentheses

-Y^2+13Y+12=0

We add all the numbers together, and all the variables

-1Y^2+13Y+12=0

a = -1; b = 13; c = +12;
Δ = b2-4ac
Δ = 132-4·(-1)·12
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{217}}{2*-1}=\frac{-13-\sqrt{217}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{217}}{2*-1}=\frac{-13+\sqrt{217}}{-2}
$