X2-12-60=-y2-4y

Solution for X2-12-60=-y2-4y equation:

X2-12-60=-X2-4X

We move all terms to the left:

X2-12-60-(-X2-4X)=0

We add all the numbers together, and all the variables

-(-1X^2-4X)+X2-12-60=0

We add all the numbers together, and all the variables

X^2-(-1X^2-4X)-72=0

We get rid of parentheses

X^2+1X^2+4X-72=0

We add all the numbers together, and all the variables

2X^2+4X-72=0

a = 2; b = 4; c = -72;
Δ = b2-4ac
Δ = 42-4·2·(-72)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{37}}{2*2}=\frac{-4-4\sqrt{37}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{37}}{2*2}=\frac{-4+4\sqrt{37}}{4}
$