8x^2-2x^2=300^2

Solution for 8x^2-2x^2=300^2 equation:

8x^2-2x^2=300^2

We move all terms to the left:

8x^2-2x^2-(300^2)=0

We add all the numbers together, and all the variables

6x^2-90000=0

a = 6; b = 0; c = -90000;
Δ = b2-4ac
Δ = 02-4·6·(-90000)
Δ = 2160000
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:

$\sqrt{\Delta}=\sqrt{2160000}=\sqrt{360000*6}=\sqrt{360000}*\sqrt{6}=600\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{6}}{2*6}=\frac{0-600\sqrt{6}}{12}
=-\frac{600\sqrt{6}}{12}
=-50\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{6}}{2*6}=\frac{0+600\sqrt{6}}{12}
=\frac{600\sqrt{6}}{12}
=50\sqrt{6}
$