15-6x2=+3x2=+23

Solution for 15-6x2=+3x2=+23 equation:

15-6x^2=+3x^2=+23

We move all terms to the left:

15-6x^2-(+3x^2)=0

We get rid of parentheses

-6x^2-3x^2+15=0

We add all the numbers together, and all the variables

-9x^2+15=0

a = -9; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-9)·15
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{15}}{2*-9}=\frac{0-6\sqrt{15}}{-18}
=-\frac{6\sqrt{15}}{-18}
=-\frac{\sqrt{15}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{15}}{2*-9}=\frac{0+6\sqrt{15}}{-18}
=\frac{6\sqrt{15}}{-18}
=\frac{\sqrt{15}}{-3}
$