30=88/w+2w

Solution for 30=88/w+2w equation:

30=88/w+2w

We move all terms to the left:

30-(88/w+2w)=0


Domain of the equation: w+2w)!=0

w∈R


We add all the numbers together, and all the variables

-(+2w+88/w)+30=0

We get rid of parentheses

-2w-88/w+30=0

We multiply all the terms by the denominator


-2w*w+30*w-88=0

We add all the numbers together, and all the variables

30w-2w*w-88=0

Wy multiply elements

-2w^2+30w-88=0

a = -2; b = 30; c = -88;
Δ = b2-4ac
Δ = 302-4·(-2)·(-88)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-14}{2*-2}=\frac{-44}{-4}
=+11
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+14}{2*-2}=\frac{-16}{-4}
=+4
$