5+3q=8/q

Solution for 5+3q=8/q equation:

5+3q=8/q

We move all terms to the left:

5+3q-(8/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

3q-(+8/q)+5=0

We get rid of parentheses

3q-8/q+5=0

We multiply all the terms by the denominator


3q*q+5*q-8=0

We add all the numbers together, and all the variables

5q+3q*q-8=0

Wy multiply elements

3q^2+5q-8=0

a = 3; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·3·(-8)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*3}=\frac{-16}{6}
=-2+2/3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*3}=\frac{6}{6}
=1
$