(100+4q^2)/(q)=81

Solution for (100+4q^2)/(q)=81 equation:

(100+4q^2)/(q)=81

We move all terms to the left:

(100+4q^2)/(q)-(81)=0


Domain of the equation: q!=0

q∈R


We multiply all the terms by the denominator


(100+4q^2)-81*q=0

We add all the numbers together, and all the variables

(100+4q^2)-81q=0

We get rid of parentheses

4q^2-81q+100=0

a = 4; b = -81; c = +100;
Δ = b2-4ac
Δ = -812-4·4·100
Δ = 4961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4961}=\sqrt{121*41}=\sqrt{121}*\sqrt{41}=11\sqrt{41}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-11\sqrt{41}}{2*4}=\frac{81-11\sqrt{41}}{8}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+11\sqrt{41}}{2*4}=\frac{81+11\sqrt{41}}{8}
$