(12)/w+9=w+13

Solution for (12)/w+9=w+13 equation:

(12)/w+9=w+13

We move all terms to the left:

(12)/w+9-(w+13)=0


Domain of the equation: w!=0

w∈R


We get rid of parentheses

12/w-w-13+9=0

We multiply all the terms by the denominator


-w*w-13*w+9*w+12=0

We add all the numbers together, and all the variables

-4w-w*w+12=0

Wy multiply elements

-1w^2-4w+12=0

a = -1; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-1}=\frac{-4}{-2}
=+2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-1}=\frac{12}{-2}
=-6
$