X^2=(4x^2)-75

Solution for X^2=(4x^2)-75 equation:

X^2=(4X^2)-75

We move all terms to the left:

X^2-((4X^2)-75)=0

We get rid of parentheses

X^2-4X^2+75=0

We add all the numbers together, and all the variables

-3X^2+75=0

a = -3; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-3)·75
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*-3}=\frac{-30}{-6}
=+5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*-3}=\frac{30}{-6}
=-5
$