Y=x2+6x-20

Solution for Y=x2+6x-20 equation:

=Y2+6Y-20

We move all terms to the left:

-(Y2+6Y-20)=0

We add all the numbers together, and all the variables

-(+Y^2+6Y-20)=0

We get rid of parentheses

-Y^2-6Y+20=0

We add all the numbers together, and all the variables

-1Y^2-6Y+20=0

a = -1; b = -6; c = +20;
Δ = b2-4ac
Δ = -62-4·(-1)·20
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*-1}=\frac{6-2\sqrt{29}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*-1}=\frac{6+2\sqrt{29}}{-2}
$