14/w=9-w

Solution for 14/w=9-w equation:

14/w=9-w

We move all terms to the left:

14/w-(9-w)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

14/w-(-1w+9)=0

We get rid of parentheses

14/w+1w-9=0

We multiply all the terms by the denominator


1w*w-9*w+14=0

We add all the numbers together, and all the variables

-9w+1w*w+14=0

Wy multiply elements

w^2-9w+14=0

a = 1; b = -9; c = +14;
Δ = b2-4ac
Δ = -92-4·1·14
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*1}=\frac{4}{2}
=2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*1}=\frac{14}{2}
=7
$