525=2w+5/w

Solution for 525=2w+5/w equation:

525=2w+5/w

We move all terms to the left:

525-(2w+5/w)=0


Domain of the equation: w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-(+2w+5/w)+525=0

We get rid of parentheses

-2w-5/w+525=0

We multiply all the terms by the denominator


-2w*w+525*w-5=0

We add all the numbers together, and all the variables

525w-2w*w-5=0

Wy multiply elements

-2w^2+525w-5=0

a = -2; b = 525; c = -5;
Δ = b2-4ac
Δ = 5252-4·(-2)·(-5)
Δ = 275585
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{-(525)-\sqrt{275585}}{2*-2}=\frac{-525-\sqrt{275585}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(525)+\sqrt{275585}}{2*-2}=\frac{-525+\sqrt{275585}}{-4}
$