-.5x^2+2x=-2.5

Solution for -.5x^2+2x=-2.5 equation:

-.5x^2+2x=-2.5

We move all terms to the left:

-.5x^2+2x-(-2.5)=0

We add all the numbers together, and all the variables

-0.5x^2+2x+2.5=0

a = -0.5; b = 2; c = +2.5;
Δ = b2-4ac
Δ = 22-4·(-0.5)·2.5
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-3}{2*-0.5}=\frac{-5}{-1}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+3}{2*-0.5}=\frac{1}{-1}
=-1
$