-6x^2+10=-13

Solution for -6x^2+10=-13 equation:

-6x^2+10=-13

We move all terms to the left:

-6x^2+10-(-13)=0

We add all the numbers together, and all the variables

-6x^2+23=0

a = -6; b = 0; c = +23;
Δ = b2-4ac
Δ = 02-4·(-6)·23
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{138}}{2*-6}=\frac{0-2\sqrt{138}}{-12}
=-\frac{2\sqrt{138}}{-12}
=-\frac{\sqrt{138}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{138}}{2*-6}=\frac{0+2\sqrt{138}}{-12}
=\frac{2\sqrt{138}}{-12}
=\frac{\sqrt{138}}{-6}
$