13-x^2=2x^2-14

Solution for 13-x^2=2x^2-14 equation:

13-x^2=2x^2-14

We move all terms to the left:

13-x^2-(2x^2-14)=0

We add all the numbers together, and all the variables

-1x^2-(2x^2-14)+13=0

We get rid of parentheses

-1x^2-2x^2+14+13=0

We add all the numbers together, and all the variables

-3x^2+27=0

a = -3; b = 0; c = +27;
Δ = b2-4ac
Δ = 02-4·(-3)·27
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*-3}=\frac{18}{-6}
=-3
$