20/q+1=q+2

Solution for 20/q+1=q+2 equation:

20/q+1=q+2

We move all terms to the left:

20/q+1-(q+2)=0


Domain of the equation: q!=0

q∈R


We get rid of parentheses

20/q-q-2+1=0

We multiply all the terms by the denominator


-q*q-2*q+1*q+20=0

We add all the numbers together, and all the variables

-1q-q*q+20=0

Wy multiply elements

-1q^2-1q+20=0

a = -1; b = -1; c = +20;
Δ = b2-4ac
Δ = -12-4·(-1)·20
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-1}=\frac{-8}{-2}
=+4
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-1}=\frac{10}{-2}
=-5
$