228/w=2w+6

Solution for 228/w=2w+6 equation:

228/w=2w+6

We move all terms to the left:

228/w-(2w+6)=0


Domain of the equation: w!=0

w∈R


We get rid of parentheses

228/w-2w-6=0

We multiply all the terms by the denominator


-2w*w-6*w+228=0

We add all the numbers together, and all the variables

-6w-2w*w+228=0

Wy multiply elements

-2w^2-6w+228=0

a = -2; b = -6; c = +228;
Δ = b2-4ac
Δ = -62-4·(-2)·228
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{465}}{2*-2}=\frac{6-2\sqrt{465}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{465}}{2*-2}=\frac{6+2\sqrt{465}}{-4}
$