(9x)^2+(18x)^2=26^2

Solution for (9x)^2+(18x)^2=26^2 equation:

(9x)^2+(18x)^2=26^2

We move all terms to the left:

(9x)^2+(18x)^2-(26^2)=0

We add all the numbers together, and all the variables

27x^2-676=0

a = 27; b = 0; c = -676;
Δ = b2-4ac
Δ = 02-4·27·(-676)
Δ = 73008
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:

$\sqrt{\Delta}=\sqrt{73008}=\sqrt{24336*3}=\sqrt{24336}*\sqrt{3}=156\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-156\sqrt{3}}{2*27}=\frac{0-156\sqrt{3}}{54}
=-\frac{156\sqrt{3}}{54}
=-\frac{26\sqrt{3}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+156\sqrt{3}}{2*27}=\frac{0+156\sqrt{3}}{54}
=\frac{156\sqrt{3}}{54}
=\frac{26\sqrt{3}}{9}
$