x2+(x+6)2=90

Solution for x2+(x+6)2=90 equation:

x2+(x+6)2=90

We move all terms to the left:

x2+(x+6)2-(90)=0

We add all the numbers together, and all the variables

x^2+(x+6)2-90=0

We multiply parentheses

x^2+2x+12-90=0

We add all the numbers together, and all the variables

x^2+2x-78=0

a = 1; b = 2; c = -78;
Δ = b2-4ac
Δ = 22-4·1·(-78)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{79}}{2*1}=\frac{-2-2\sqrt{79}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{79}}{2*1}=\frac{-2+2\sqrt{79}}{2}
$