-11x^2=-7

Solution for -11x^2=-7 equation:

-11x^2=-7

We move all terms to the left:

-11x^2-(-7)=0

We add all the numbers together, and all the variables

-11x^2+7=0

a = -11; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-11)·7
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{77}}{2*-11}=\frac{0-2\sqrt{77}}{-22}
=-\frac{2\sqrt{77}}{-22}
=-\frac{\sqrt{77}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{77}}{2*-11}=\frac{0+2\sqrt{77}}{-22}
=\frac{2\sqrt{77}}{-22}
=\frac{\sqrt{77}}{-11}
$