-77+10x^2=-x^2

Solution for -77+10x^2=-x^2 equation:

-77+10x^2=-x^2

We move all terms to the left:

-77+10x^2-(-x^2)=0

We get rid of parentheses

10x^2+x^2-77=0

We add all the numbers together, and all the variables

11x^2-77=0

a = 11; b = 0; c = -77;
Δ = b2-4ac
Δ = 02-4·11·(-77)
Δ = 3388
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:

$\sqrt{\Delta}=\sqrt{3388}=\sqrt{484*7}=\sqrt{484}*\sqrt{7}=22\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{7}}{2*11}=\frac{0-22\sqrt{7}}{22}
=-\frac{22\sqrt{7}}{22}
=-\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{7}}{2*11}=\frac{0+22\sqrt{7}}{22}
=\frac{22\sqrt{7}}{22}
=\sqrt{7}
$