8q=36/q+4q

Solution for 8q=36/q+4q equation:

8q=36/q+4q

We move all terms to the left:

8q-(36/q+4q)=0


Domain of the equation: q+4q)!=0

q∈R


We add all the numbers together, and all the variables

8q-(+4q+36/q)=0

We get rid of parentheses

8q-4q-36/q=0

We multiply all the terms by the denominator


8q*q-4q*q-36=0

Wy multiply elements

8q^2-4q^2-36=0

We add all the numbers together, and all the variables

4q^2-36=0

a = 4; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·4·(-36)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*4}=\frac{-24}{8}
=-3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*4}=\frac{24}{8}
=3
$