(21/w)-w=4

Solution for (21/w)-w=4 equation:

(21/w)-w=4

We move all terms to the left:

(21/w)-w-(4)=0


Domain of the equation: w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

(+21/w)-w-4=0

We add all the numbers together, and all the variables

-1w+(+21/w)-4=0

We get rid of parentheses

-1w+21/w-4=0

We multiply all the terms by the denominator


-1w*w-4*w+21=0

We add all the numbers together, and all the variables

-4w-1w*w+21=0

Wy multiply elements

-1w^2-4w+21=0

a = -1; b = -4; c = +21;
Δ = b2-4ac
Δ = -42-4·(-1)·21
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*-1}=\frac{-6}{-2}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*-1}=\frac{14}{-2}
=-7
$