12x^2-64=-x^2

Solution for 12x^2-64=-x^2 equation:

12x^2-64=-x^2

We move all terms to the left:

12x^2-64-(-x^2)=0

We get rid of parentheses

12x^2+x^2-64=0

We add all the numbers together, and all the variables

13x^2-64=0

a = 13; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·13·(-64)
Δ = 3328
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:

$\sqrt{\Delta}=\sqrt{3328}=\sqrt{256*13}=\sqrt{256}*\sqrt{13}=16\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{13}}{2*13}=\frac{0-16\sqrt{13}}{26}
=-\frac{16\sqrt{13}}{26}
=-\frac{8\sqrt{13}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{13}}{2*13}=\frac{0+16\sqrt{13}}{26}
=\frac{16\sqrt{13}}{26}
=\frac{8\sqrt{13}}{13}
$