10x^2+x^2=366^2

Solution for 10x^2+x^2=366^2 equation:

10x^2+x^2=366^2

We move all terms to the left:

10x^2+x^2-(366^2)=0

We add all the numbers together, and all the variables

11x^2-133956=0

a = 11; b = 0; c = -133956;
Δ = b2-4ac
Δ = 02-4·11·(-133956)
Δ = 5894064
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:

$\sqrt{\Delta}=\sqrt{5894064}=\sqrt{535824*11}=\sqrt{535824}*\sqrt{11}=732\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-732\sqrt{11}}{2*11}=\frac{0-732\sqrt{11}}{22}
=-\frac{732\sqrt{11}}{22}
=-\frac{366\sqrt{11}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+732\sqrt{11}}{2*11}=\frac{0+732\sqrt{11}}{22}
=\frac{732\sqrt{11}}{22}
=\frac{366\sqrt{11}}{11}
$