0=x^2-4x-92

Solution for 0=x^2-4x-92 equation:

0=x^2-4x-92

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+4x+92=0

We add all the numbers together, and all the variables

-1x^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}
$