Y=x2+5x-20Y=x-8

Solution for Y=x2+5x-20Y=x-8 equation:

=Y2+5Y-20=Y-8

We move all terms to the left:

-(Y2+5Y-20)=0

We add all the numbers together, and all the variables

-(+Y^2+5Y-20)=0

We get rid of parentheses

-Y^2-5Y+20=0

We add all the numbers together, and all the variables

-1Y^2-5Y+20=0

a = -1; b = -5; c = +20;
Δ = b2-4ac
Δ = -52-4·(-1)·20
Δ = 105
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{-(-5)-\sqrt{105}}{2*-1}=\frac{5-\sqrt{105}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*-1}=\frac{5+\sqrt{105}}{-2}
$