X2+2x2=75^2

Solution for X2+2x2=75^2 equation:

X2+2X^2=75^2

We move all terms to the left:

X2+2X^2-(75^2)=0

We add all the numbers together, and all the variables

3X^2-5625=0

a = 3; b = 0; c = -5625;
Δ = b2-4ac
Δ = 02-4·3·(-5625)
Δ = 67500
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:

$\sqrt{\Delta}=\sqrt{67500}=\sqrt{22500*3}=\sqrt{22500}*\sqrt{3}=150\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150\sqrt{3}}{2*3}=\frac{0-150\sqrt{3}}{6}
=-\frac{150\sqrt{3}}{6}
=-25\sqrt{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150\sqrt{3}}{2*3}=\frac{0+150\sqrt{3}}{6}
=\frac{150\sqrt{3}}{6}
=25\sqrt{3}
$