-0,5x^2+2,5x=-3

Solution for -0,5x^2+2,5x=-3 equation:

-0.5x^2+2.5x=-3

We move all terms to the left:

-0.5x^2+2.5x-(-3)=0

We add all the numbers together, and all the variables

-0.5x^2+2.5x+3=0

a = -0.5; b = 2.5; c = +3;
Δ = b2-4ac
Δ = 2.52-4·(-0.5)·3
Δ = 12.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2.5)-\sqrt{12.25}}{2*-0.5}=\frac{-2.5-\sqrt{12.25}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{12.25}}{2*-0.5}=\frac{-2.5+\sqrt{12.25}}{-1}
$