(100+4q^2)/(q)=8q

Solution for (100+4q^2)/(q)=8q equation:

(100+4q^2)/(q)=8q

We move all terms to the left:

(100+4q^2)/(q)-(8q)=0


Domain of the equation: q!=0

q∈R


We multiply all the terms by the denominator


(100+4q^2)-8q*q=0

Wy multiply elements

(100+4q^2)-8q^2=0

We get rid of parentheses

4q^2-8q^2+100=0

We add all the numbers together, and all the variables

-4q^2+100=0

a = -4; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-4)·100
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*-4}=\frac{-40}{-8}
=+5
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*-4}=\frac{40}{-8}
=-5
$