4q+(100/q)=8q

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

4q+(100/q)=8q

We move all terms to the left:

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


Domain of the equation: q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-4q+(+100/q)=0

We get rid of parentheses

-4q+100/q=0

We multiply all the terms by the denominator


-4q*q+100=0

Wy multiply elements

-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
$