0.1q=50/q

Solution for 0.1q=50/q equation:

0.1q=50/q

We move all terms to the left:

0.1q-(50/q)=0


Domain of the equation: q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

0.1q-(+50/q)=0

We get rid of parentheses

0.1q-50/q=0

We multiply all the terms by the denominator


(0.1q)*q-50=0

We add all the numbers together, and all the variables

(+0.1q)*q-50=0

We multiply parentheses

0q^2-50=0

We add all the numbers together, and all the variables

q^2-50=0

a = 1; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·1·(-50)
Δ = 200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*1}=\frac{0-10\sqrt{2}}{2}
=-\frac{10\sqrt{2}}{2}
=-5\sqrt{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*1}=\frac{0+10\sqrt{2}}{2}
=\frac{10\sqrt{2}}{2}
=5\sqrt{2}
$