(X2+y)2=26

Solution for (X2+y)2=26 equation:

(X2+X)2=26

We move all terms to the left:

(X2+X)2-(26)=0

We add all the numbers together, and all the variables

(+X^2+X)2-26=0

We multiply parentheses

2X^2+2X-26=0

a = 2; b = 2; c = -26;
Δ = b2-4ac
Δ = 22-4·2·(-26)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{53}}{2*2}=\frac{-2-2\sqrt{53}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{53}}{2*2}=\frac{-2+2\sqrt{53}}{4}
$