-2x^2+1/2=-17.5

Solution for -2x^2+1/2=-17.5 equation:

-2x^2+1/2=-17.5

We move all terms to the left:

-2x^2+1/2-(-17.5)=0

We add all the numbers together, and all the variables

-2x^2+17.5+1/2=0

We multiply all the terms by the denominator


-2x^2*2+1+(17.5)*2=0

We add all the numbers together, and all the variables

-2x^2*2+36=0

Wy multiply elements

-4x^2+36=0

a = -4; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-4)·36
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-4}=\frac{24}{-8}
=-3
$