X^2-7=4x^2-8

Solution for X^2-7=4x^2-8 equation:

X^2-7=4X^2-8

We move all terms to the left:

X^2-7-(4X^2-8)=0

We get rid of parentheses

X^2-4X^2+8-7=0

We add all the numbers together, and all the variables

-3X^2+1=0

a = -3; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-3)·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*-3}=\frac{0-2\sqrt{3}}{-6}
=-\frac{2\sqrt{3}}{-6}
=-\frac{\sqrt{3}}{-3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*-3}=\frac{0+2\sqrt{3}}{-6}
=\frac{2\sqrt{3}}{-6}
=\frac{\sqrt{3}}{-3}
$