6x^2+5x^2=187

Solution for 6x^2+5x^2=187 equation:

6x^2+5x^2=187

We move all terms to the left:

6x^2+5x^2-(187)=0

We add all the numbers together, and all the variables

11x^2-187=0

a = 11; b = 0; c = -187;
Δ = b2-4ac
Δ = 02-4·11·(-187)
Δ = 8228
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:

$\sqrt{\Delta}=\sqrt{8228}=\sqrt{484*17}=\sqrt{484}*\sqrt{17}=22\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{17}}{2*11}=\frac{0-22\sqrt{17}}{22}
=-\frac{22\sqrt{17}}{22}
=-\sqrt{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{17}}{2*11}=\frac{0+22\sqrt{17}}{22}
=\frac{22\sqrt{17}}{22}
=\sqrt{17}
$