14-(8/w)=w+23

Solution for 14-(8/w)=w+23 equation:

14-(8/w)=w+23

We move all terms to the left:

14-(8/w)-(w+23)=0


Domain of the equation: w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-(+8/w)-(w+23)+14=0

We get rid of parentheses

-8/w-w-23+14=0

We multiply all the terms by the denominator


-w*w-23*w+14*w-8=0

We add all the numbers together, and all the variables

-9w-w*w-8=0

Wy multiply elements

-1w^2-9w-8=0

a = -1; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·(-1)·(-8)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*-1}=\frac{2}{-2}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*-1}=\frac{16}{-2}
=-8
$