X(2)+(24+y)2=84

Solution for X(2)+(24+y)2=84 equation:

X(2)+(24+X)2=84

We move all terms to the left:

X(2)+(24+X)2-(84)=0

We add all the numbers together, and all the variables

X2+(X+24)2-84=0

We add all the numbers together, and all the variables

X^2+(X+24)2-84=0

We multiply parentheses

X^2+2X+48-84=0

We add all the numbers together, and all the variables

X^2+2X-36=0

a = 1; b = 2; c = -36;
Δ = b2-4ac
Δ = 22-4·1·(-36)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*1}=\frac{-2-2\sqrt{37}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*1}=\frac{-2+2\sqrt{37}}{2}
$