6w=30/w=5

Solution for 6w=30/w=5 equation:

6w=30/w=5

We move all terms to the left:

6w-(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

6w-(+30/w)=0

We get rid of parentheses

6w-30/w=0

We multiply all the terms by the denominator


6w*w-30=0

Wy multiply elements

6w^2-30=0

a = 6; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·6·(-30)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*6}=\frac{0-12\sqrt{5}}{12}
=-\frac{12\sqrt{5}}{12}
=-\sqrt{5}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*6}=\frac{0+12\sqrt{5}}{12}
=\frac{12\sqrt{5}}{12}
=\sqrt{5}
$