2q+80=q+80+100/q

Solution for 2q+80=q+80+100/q equation:

2q+80=q+80+100/q

We move all terms to the left:

2q+80-(q+80+100/q)=0


Domain of the equation: q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

2q-(q+100/q+80)+80=0

We get rid of parentheses

2q-q-100/q-80+80=0

We multiply all the terms by the denominator


2q*q-q*q-80*q+80*q-100=0

We add all the numbers together, and all the variables

2q*q-q*q-100=0

Wy multiply elements

2q^2-1q^2-100=0

We add all the numbers together, and all the variables

q^2-100=0

a = 1; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·1·(-100)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*1}=\frac{-20}{2}
=-10
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*1}=\frac{20}{2}
=10
$