X^2+5=3x^2-7

Solution for X^2+5=3x^2-7 equation:

X^2+5=3X^2-7

We move all terms to the left:

X^2+5-(3X^2-7)=0

We get rid of parentheses

X^2-3X^2+7+5=0

We add all the numbers together, and all the variables

-2X^2+12=0

a = -2; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-2)·12
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-2}=\frac{0-4\sqrt{6}}{-4}
=-\frac{4\sqrt{6}}{-4}
=-\frac{\sqrt{6}}{-1}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-2}=\frac{0+4\sqrt{6}}{-4}
=\frac{4\sqrt{6}}{-4}
=\frac{\sqrt{6}}{-1}
$