0=-0.5*x^2+1.5*x+10

Solution for 0=-0.5*x^2+1.5*x+10 equation:

0=-0.5x^2+1.5x+10

We move all terms to the left:

0-(-0.5x^2+1.5x+10)=0

We add all the numbers together, and all the variables

-(-0.5x^2+1.5x+10)=0

We get rid of parentheses

0.5x^2-1.5x-10=0

a = 0.5; b = -1.5; c = -10;
Δ = b2-4ac
Δ = -1.52-4·0.5·(-10)
Δ = 22.25
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{-(-1.5)-\sqrt{22.25}}{2*0.5}=\frac{1.5-\sqrt{22.25}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{22.25}}{2*0.5}=\frac{1.5+\sqrt{22.25}}{1}
$