5w+5/w-11=2

Solution for 5w+5/w-11=2 equation:

5w+5/w-11=2

We move all terms to the left:

5w+5/w-11-(2)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

5w+5/w-13=0

We multiply all the terms by the denominator


5w*w-13*w+5=0

We add all the numbers together, and all the variables

-13w+5w*w+5=0

Wy multiply elements

5w^2-13w+5=0

a = 5; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·5·5
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{69}}{2*5}=\frac{13-\sqrt{69}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{69}}{2*5}=\frac{13+\sqrt{69}}{10}
$