.5q^2=5q

Solution for .5q^2=5q equation:

.5q^2=5q

We move all terms to the left:

.5q^2-(5q)=0

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

$\sqrt{\Delta}=\sqrt{25}=5$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*.5}=\frac{0}{1}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*.5}=\frac{10}{1}
=10
$