6x^2+3x^2=117

Solution for 6x^2+3x^2=117 equation:

6x^2+3x^2=117

We move all terms to the left:

6x^2+3x^2-(117)=0

We add all the numbers together, and all the variables

9x^2-117=0

a = 9; b = 0; c = -117;
Δ = b2-4ac
Δ = 02-4·9·(-117)
Δ = 4212
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:

$\sqrt{\Delta}=\sqrt{4212}=\sqrt{324*13}=\sqrt{324}*\sqrt{13}=18\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{13}}{2*9}=\frac{0-18\sqrt{13}}{18}
=-\frac{18\sqrt{13}}{18}
=-\sqrt{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{13}}{2*9}=\frac{0+18\sqrt{13}}{18}
=\frac{18\sqrt{13}}{18}
=\sqrt{13}
$