0.5x=-0.0625x^2+5.5x

Solution for 0.5x=-0.0625x^2+5.5x equation:

0.5x=-0.0625x^2+5.5x

We move all terms to the left:

0.5x-(-0.0625x^2+5.5x)=0

We get rid of parentheses

0.0625x^2-5.5x+0.5x=0

We add all the numbers together, and all the variables

0.0625x^2-5x=0

a = 0.0625; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·0.0625·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*0.0625}=\frac{0}{0.125}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*0.0625}=\frac{10}{0.125}
=80
$