-2x^2+12x-10=-24

Solution for -2x^2+12x-10=-24 equation:

-2x^2+12x-10=-24

We move all terms to the left:

-2x^2+12x-10-(-24)=0

We add all the numbers together, and all the variables

-2x^2+12x+14=0

a = -2; b = 12; c = +14;
Δ = b2-4ac
Δ = 122-4·(-2)·14
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-16}{2*-2}=\frac{-28}{-4}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+16}{2*-2}=\frac{4}{-4}
=-1
$