10q=1000/q

Solution for 10q=1000/q equation:

10q=1000/q

We move all terms to the left:

10q-(1000/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

10q-(+1000/q)=0

We get rid of parentheses

10q-1000/q=0

We multiply all the terms by the denominator


10q*q-1000=0

Wy multiply elements

10q^2-1000=0

a = 10; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·10·(-1000)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200}{2*10}=\frac{-200}{20}
=-10
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200}{2*10}=\frac{200}{20}
=10
$