-.5x^2+2.5x+1=0

Solution for -.5x^2+2.5x+1=0 equation:

-.5x^2+2.5x+1=0

We add all the numbers together, and all the variables

-0.5x^2+2.5x+1=0

a = -0.5; b = 2.5; c = +1;
Δ = b2-4ac
Δ = 2.52-4·(-0.5)·1
Δ = 8.25
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{8.25}}{2*-0.5}=\frac{-2.5-\sqrt{8.25}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{8.25}}{2*-0.5}=\frac{-2.5+\sqrt{8.25}}{-1}
$