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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

9x^2-23=0

a = 9; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·9·(-23)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{23}}{2*9}=\frac{0-6\sqrt{23}}{18}
=-\frac{6\sqrt{23}}{18}
=-\frac{\sqrt{23}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{23}}{2*9}=\frac{0+6\sqrt{23}}{18}
=\frac{6\sqrt{23}}{18}
=\frac{\sqrt{23}}{3}
$