10=-0.5x^2+0.1x+26.9

Solution for 10=-0.5x^2+0.1x+26.9 equation:

10=-0.5x^2+0.1x+26.9

We move all terms to the left:

10-(-0.5x^2+0.1x+26.9)=0

We get rid of parentheses

0.5x^2-0.1x-26.9+10=0

We add all the numbers together, and all the variables

0.5x^2-0.1x-16.9=0

a = 0.5; b = -0.1; c = -16.9;
Δ = b2-4ac
Δ = -0.12-4·0.5·(-16.9)
Δ = 33.81
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{-(-0.1)-\sqrt{33.81}}{2*0.5}=\frac{0.1-\sqrt{33.81}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{33.81}}{2*0.5}=\frac{0.1+\sqrt{33.81}}{1}
$