X^2-6=-5x^2+378

Solution for X^2-6=-5x^2+378 equation:

X^2-6=-5X^2+378

We move all terms to the left:

X^2-6-(-5X^2+378)=0

We get rid of parentheses

X^2+5X^2-378-6=0

We add all the numbers together, and all the variables

6X^2-384=0

a = 6; b = 0; c = -384;
Δ = b2-4ac
Δ = 02-4·6·(-384)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96}{2*6}=\frac{-96}{12}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*6}=\frac{96}{12}
=8
$