2w+10/10w=5

Solution for 2w+10/10w=5 equation:

2w+10/10w=5

We move all terms to the left:

2w+10/10w-(5)=0


Domain of the equation: 10w!=0

w!=0/10

w!=0

w∈R


We multiply all the terms by the denominator


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

Wy multiply elements

20w^2-50w+10=0

a = 20; b = -50; c = +10;
Δ = b2-4ac
Δ = -502-4·20·10
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{17}}{2*20}=\frac{50-10\sqrt{17}}{40}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{17}}{2*20}=\frac{50+10\sqrt{17}}{40}
$