2x^2=x^2+367

Solution for 2x^2=x^2+367 equation:

2x^2=x^2+367

We move all terms to the left:

2x^2-(x^2+367)=0

We get rid of parentheses

2x^2-x^2-367=0

We add all the numbers together, and all the variables

x^2-367=0

a = 1; b = 0; c = -367;
Δ = b2-4ac
Δ = 02-4·1·(-367)
Δ = 1468
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:

$\sqrt{\Delta}=\sqrt{1468}=\sqrt{4*367}=\sqrt{4}*\sqrt{367}=2\sqrt{367}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{367}}{2*1}=\frac{0-2\sqrt{367}}{2}
=-\frac{2\sqrt{367}}{2}
=-\sqrt{367}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{367}}{2*1}=\frac{0+2\sqrt{367}}{2}
=\frac{2\sqrt{367}}{2}
=\sqrt{367}
$