-2x^2+36x-10=24

Solution for -2x^2+36x-10=24 equation:

-2x^2+36x-10=24

We move all terms to the left:

-2x^2+36x-10-(24)=0

We add all the numbers together, and all the variables

-2x^2+36x-34=0

a = -2; b = 36; c = -34;
Δ = b2-4ac
Δ = 362-4·(-2)·(-34)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-32}{2*-2}=\frac{-68}{-4}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+32}{2*-2}=\frac{-4}{-4}
=1
$