Y=x^2+20x+97

Solution for Y=x^2+20x+97 equation:

=Y^2+20Y+97

We move all terms to the left:

-(Y^2+20Y+97)=0

We get rid of parentheses

-Y^2-20Y-97=0

We add all the numbers together, and all the variables

-1Y^2-20Y-97=0

a = -1; b = -20; c = -97;
Δ = b2-4ac
Δ = -202-4·(-1)·(-97)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{3}}{2*-1}=\frac{20-2\sqrt{3}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{3}}{2*-1}=\frac{20+2\sqrt{3}}{-2}
$