-3+13x^2=2(x^2+3)

Solution for -3+13x^2=2(x^2+3) equation:

-3+13x^2=2(x^2+3)

We move all terms to the left:

-3+13x^2-(2(x^2+3))=0


We calculate terms in parentheses: -(2(x^2+3)), so:

2(x^2+3)

We multiply parentheses

2x^2+6

Back to the equation:

-(2x^2+6)


We get rid of parentheses

13x^2-2x^2-6-3=0

We add all the numbers together, and all the variables

11x^2-9=0

a = 11; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·11·(-9)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{11}}{2*11}=\frac{0-6\sqrt{11}}{22}
=-\frac{6\sqrt{11}}{22}
=-\frac{3\sqrt{11}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{11}}{2*11}=\frac{0+6\sqrt{11}}{22}
=\frac{6\sqrt{11}}{22}
=\frac{3\sqrt{11}}{11}
$