5w+1/w-7=2

Solution for 5w+1/w-7=2 equation:

5w+1/w-7=2

We move all terms to the left:

5w+1/w-7-(2)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

5w+1/w-9=0

We multiply all the terms by the denominator


5w*w-9*w+1=0

We add all the numbers together, and all the variables

-9w+5w*w+1=0

Wy multiply elements

5w^2-9w+1=0

a = 5; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·5·1
Δ = 61
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{-(-9)-\sqrt{61}}{2*5}=\frac{9-\sqrt{61}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{61}}{2*5}=\frac{9+\sqrt{61}}{10}
$