7=w-30/w

Solution for 7=w-30/w equation:

7=w-30/w

We move all terms to the left:

7-(w-30/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

-(+w-30/w)+7=0

We get rid of parentheses

-w+30/w+7=0

We multiply all the terms by the denominator


-w*w+7*w+30=0

We add all the numbers together, and all the variables

7w-w*w+30=0

Wy multiply elements

-1w^2+7w+30=0

a = -1; b = 7; c = +30;
Δ = b2-4ac
Δ = 72-4·(-1)·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-1}=\frac{-20}{-2}
=+10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-1}=\frac{6}{-2}
=-3
$