2w+5/w-1=9

Solution for 2w+5/w-1=9 equation:

2w+5/w-1=9

We move all terms to the left:

2w+5/w-1-(9)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

2w+5/w-10=0

We multiply all the terms by the denominator


2w*w-10*w+5=0

We add all the numbers together, and all the variables

-10w+2w*w+5=0

Wy multiply elements

2w^2-10w+5=0

a = 2; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·2·5
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*2}=\frac{10-2\sqrt{15}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*2}=\frac{10+2\sqrt{15}}{4}
$