14+-6x^2-3x^2=-8

Solution for 14+-6x^2-3x^2=-8 equation:

14+-6x^2-3x^2=-8

We move all terms to the left:

14+-6x^2-3x^2-(-8)=0

We add all the numbers together, and all the variables

-9x^2+22=0

a = -9; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-9)·22
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{22}}{2*-9}=\frac{0-6\sqrt{22}}{-18}
=-\frac{6\sqrt{22}}{-18}
=-\frac{\sqrt{22}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{22}}{2*-9}=\frac{0+6\sqrt{22}}{-18}
=\frac{6\sqrt{22}}{-18}
=\frac{\sqrt{22}}{-3}
$