(6*6)+(11*11)=x*x

Solution for (6*6)+(11*11)=x*x equation:

(6*6)+(11*11)=x*x

We move all terms to the left:

(6*6)+(11*11)-(x*x)=0

We add all the numbers together, and all the variables

-(+x*x)+36+121=0

We add all the numbers together, and all the variables

-(+x*x)+157=0

We get rid of parentheses

-x*x+157=0

Wy multiply elements

-1x^2+157=0

a = -1; b = 0; c = +157;
Δ = b2-4ac
Δ = 02-4·(-1)·157
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{157}}{2*-1}=\frac{0-2\sqrt{157}}{-2}
=-\frac{2\sqrt{157}}{-2}
=-\frac{\sqrt{157}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{157}}{2*-1}=\frac{0+2\sqrt{157}}{-2}
=\frac{2\sqrt{157}}{-2}
=\frac{\sqrt{157}}{-1}
$