-2x2+24x=-92

Solution for -2x2+24x=-92 equation:

-2x^2+24x=-92

We move all terms to the left:

-2x^2+24x-(-92)=0

We add all the numbers together, and all the variables

-2x^2+24x+92=0

a = -2; b = 24; c = +92;
Δ = b2-4ac
Δ = 242-4·(-2)·92
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{82}}{2*-2}=\frac{-24-4\sqrt{82}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{82}}{2*-2}=\frac{-24+4\sqrt{82}}{-4}
$