5/(12+3w)=w

Solution for 5/(12+3w)=w equation:

5/(12+3w)=w

We move all terms to the left:

5/(12+3w)-(w)=0


Domain of the equation: (12+3w)!=0

We move all terms containing w to the left, all other terms to the right

3w!=-12

w!=-12/3

w!=-4

w∈R


We add all the numbers together, and all the variables

5/(3w+12)-w=0

We add all the numbers together, and all the variables

-1w+5/(3w+12)=0

We multiply all the terms by the denominator


-1w*(3w+12)+5=0

We multiply parentheses

-3w^2-12w+5=0

a = -3; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·(-3)·5
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{51}}{2*-3}=\frac{12-2\sqrt{51}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{51}}{2*-3}=\frac{12+2\sqrt{51}}{-6}
$