5x^2+6x^2=165

Solution for 5x^2+6x^2=165 equation:

5x^2+6x^2=165

We move all terms to the left:

5x^2+6x^2-(165)=0

We add all the numbers together, and all the variables

11x^2-165=0

a = 11; b = 0; c = -165;
Δ = b2-4ac
Δ = 02-4·11·(-165)
Δ = 7260
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:

$\sqrt{\Delta}=\sqrt{7260}=\sqrt{484*15}=\sqrt{484}*\sqrt{15}=22\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{15}}{2*11}=\frac{0-22\sqrt{15}}{22}
=-\frac{22\sqrt{15}}{22}
=-\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{15}}{2*11}=\frac{0+22\sqrt{15}}{22}
=\frac{22\sqrt{15}}{22}
=\sqrt{15}
$