x^2-92=-4x

Solution for x^2-92=-4x equation:

x^2-92=-4x

We move all terms to the left:

x^2-92-(-4x)=0

We get rid of parentheses

x^2+4x-92=0

a = 1; b = 4; c = -92;
Δ = b2-4ac
Δ = 42-4·1·(-92)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{6}}{2*1}=\frac{-4-8\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{6}}{2*1}=\frac{-4+8\sqrt{6}}{2}
$