8q=36+4q^2/q

Solution for 8q=36+4q^2/q equation:

8q=36+4q^2/q

We move all terms to the left:

8q-(36+4q^2/q)=0


Domain of the equation: q)!=0

q!=0/1

q!=0

q∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

4q^2-36q=0

a = 4; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·4·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*4}=\frac{0}{8}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*4}=\frac{72}{8}
=9
$