(12x)2+4=(5x)2+8

Solution for (12x)2+4=(5x)2+8 equation:

(12x)2+4=(5x)2+8

We move all terms to the left:

(12x)2+4-((5x)2+8)=0

We add all the numbers together, and all the variables

-(+5x^2+8)+12x2+4=0

We add all the numbers together, and all the variables

12x^2-(+5x^2+8)+4=0

We get rid of parentheses

12x^2-5x^2-8+4=0

We add all the numbers together, and all the variables

7x^2-4=0

a = 7; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·7·(-4)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*7}=\frac{0-4\sqrt{7}}{14}
=-\frac{4\sqrt{7}}{14}
=-\frac{2\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*7}=\frac{0+4\sqrt{7}}{14}
=\frac{4\sqrt{7}}{14}
=\frac{2\sqrt{7}}{7}
$