8x^2=144+x^2

Solution for 8x^2=144+x^2 equation:

8x^2=144+x^2

We move all terms to the left:

8x^2-(144+x^2)=0

We get rid of parentheses

8x^2-x^2-144=0

We add all the numbers together, and all the variables

7x^2-144=0

a = 7; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·7·(-144)
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{7}}{2*7}=\frac{0-24\sqrt{7}}{14}
=-\frac{24\sqrt{7}}{14}
=-\frac{12\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{7}}{2*7}=\frac{0+24\sqrt{7}}{14}
=\frac{24\sqrt{7}}{14}
=\frac{12\sqrt{7}}{7}
$