0=(100-q)*q-10q

Solution for 0=(100-q)*q-10q equation:

0=(100-q)*q-10q

We move all terms to the left:

0-((100-q)*q-10q)=0

We add all the numbers together, and all the variables

-((-1q+100)*q-10q)+0=0

We add all the numbers together, and all the variables

-((-1q+100)*q-10q)=0


We calculate terms in parentheses: -((-1q+100)*q-10q), so:

(-1q+100)*q-10q

We add all the numbers together, and all the variables

-10q+(-1q+100)*q

We multiply parentheses

-1q^2-10q+100q

We add all the numbers together, and all the variables

-1q^2+90q

Back to the equation:

-(-1q^2+90q)


We get rid of parentheses

1q^2-90q=0

We add all the numbers together, and all the variables

q^2-90q=0

a = 1; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·1·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*1}=\frac{0}{2}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*1}=\frac{180}{2}
=90
$