10=-0.5x^2+6x

Solution for 10=-0.5x^2+6x equation:

10=-0.5x^2+6x

We move all terms to the left:

10-(-0.5x^2+6x)=0

We get rid of parentheses

0.5x^2-6x+10=0

a = 0.5; b = -6; c = +10;
Δ = b2-4ac
Δ = -62-4·0.5·10
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*0.5}=\frac{2}{1}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*0.5}=\frac{10}{1}
=10
$