30+2q=200/q

Solution for 30+2q=200/q equation:

30+2q=200/q

We move all terms to the left:

30+2q-(200/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

2q-(+200/q)+30=0

We get rid of parentheses

2q-200/q+30=0

We multiply all the terms by the denominator


2q*q+30*q-200=0

We add all the numbers together, and all the variables

30q+2q*q-200=0

Wy multiply elements

2q^2+30q-200=0

a = 2; b = 30; c = -200;
Δ = b2-4ac
Δ = 302-4·2·(-200)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-50}{2*2}=\frac{-80}{4}
=-20
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+50}{2*2}=\frac{20}{4}
=5
$