10=5x+0.125x^2

Solution for 10=5x+0.125x^2 equation:

10=5x+0.125x^2

We move all terms to the left:

10-(5x+0.125x^2)=0

We get rid of parentheses

-0.125x^2-5x+10=0

a = -0.125; b = -5; c = +10;
Δ = b2-4ac
Δ = -52-4·(-0.125)·10
Δ = 30
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{-(-5)-\sqrt{30}}{2*-0.125}=\frac{5-\sqrt{30}}{-0.25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{30}}{2*-0.125}=\frac{5+\sqrt{30}}{-0.25}
$