3x^2+2x^2=26^2

Solution for 3x^2+2x^2=26^2 equation:

3x^2+2x^2=26^2

We move all terms to the left:

3x^2+2x^2-(26^2)=0

We add all the numbers together, and all the variables

5x^2-676=0

a = 5; b = 0; c = -676;
Δ = b2-4ac
Δ = 02-4·5·(-676)
Δ = 13520
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:

$\sqrt{\Delta}=\sqrt{13520}=\sqrt{2704*5}=\sqrt{2704}*\sqrt{5}=52\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52\sqrt{5}}{2*5}=\frac{0-52\sqrt{5}}{10}
=-\frac{52\sqrt{5}}{10}
=-\frac{26\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52\sqrt{5}}{2*5}=\frac{0+52\sqrt{5}}{10}
=\frac{52\sqrt{5}}{10}
=\frac{26\sqrt{5}}{5}
$