0.5q+8=(0.25q+8+16)q

Solution for 0.5q+8=(0.25q+8+16)q equation:

0.5q+8=(0.25q+8+16)q

We move all terms to the left:

0.5q+8-((0.25q+8+16)q)=0

We add all the numbers together, and all the variables

0.5q-((0.25q+24)q)+8=0


We calculate terms in parentheses: -((0.25q+24)q), so:

(0.25q+24)q

We multiply parentheses

0q^2+24q

We add all the numbers together, and all the variables

q^2+24q

Back to the equation:

-(q^2+24q)


We get rid of parentheses

-q^2+0.5q-24q+8=0

We add all the numbers together, and all the variables

-1q^2-23.5q+8=0

a = -1; b = -23.5; c = +8;
Δ = b2-4ac
Δ = -23.52-4·(-1)·8
Δ = 584.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23.5)-\sqrt{584.25}}{2*-1}=\frac{23.5-\sqrt{584.25}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23.5)+\sqrt{584.25}}{2*-1}=\frac{23.5+\sqrt{584.25}}{-2}
$