Y=x2+13x+8

Solution for Y=x2+13x+8 equation:

=Y2+13Y+8

We move all terms to the left:

-(Y2+13Y+8)=0

We add all the numbers together, and all the variables

-(+Y^2+13Y+8)=0

We get rid of parentheses

-Y^2-13Y-8=0

We add all the numbers together, and all the variables

-1Y^2-13Y-8=0

a = -1; b = -13; c = -8;
Δ = b2-4ac
Δ = -132-4·(-1)·(-8)
Δ = 137
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{137}}{2*-1}=\frac{13-\sqrt{137}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{137}}{2*-1}=\frac{13+\sqrt{137}}{-2}
$