11x^2=x^2+8

Solution for 11x^2=x^2+8 equation:

11x^2=x^2+8

We move all terms to the left:

11x^2-(x^2+8)=0

We get rid of parentheses

11x^2-x^2-8=0

We add all the numbers together, and all the variables

10x^2-8=0

a = 10; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·10·(-8)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*10}=\frac{0-8\sqrt{5}}{20}
=-\frac{8\sqrt{5}}{20}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*10}=\frac{0+8\sqrt{5}}{20}
=\frac{8\sqrt{5}}{20}
=\frac{2\sqrt{5}}{5}
$