x^2-7=23-10x^2

Solution for x^2-7=23-10x^2 equation:

x^2-7=23-10x^2

We move all terms to the left:

x^2-7-(23-10x^2)=0

We get rid of parentheses

x^2+10x^2-23-7=0

We add all the numbers together, and all the variables

11x^2-30=0

a = 11; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·11·(-30)
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{330}}{2*11}=\frac{0-2\sqrt{330}}{22}
=-\frac{2\sqrt{330}}{22}
=-\frac{\sqrt{330}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{330}}{2*11}=\frac{0+2\sqrt{330}}{22}
=\frac{2\sqrt{330}}{22}
=\frac{\sqrt{330}}{11}
$