(X^2)-(8y)=121.5

Solution for (X^2)-(8y)=121.5 equation:

(X^2)-(8X)=121.5

We move all terms to the left:

(X^2)-(8X)-(121.5)=0

We add all the numbers together, and all the variables

X^2-8X-121.5=0

a = 1; b = -8; c = -121.5;
Δ = b2-4ac
Δ = -82-4·1·(-121.5)
Δ = 550
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{550}=\sqrt{25*22}=\sqrt{25}*\sqrt{22}=5\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-5\sqrt{22}}{2*1}=\frac{8-5\sqrt{22}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+5\sqrt{22}}{2*1}=\frac{8+5\sqrt{22}}{2}
$