39/w=3w=

Solution for 39/w=3w= equation:

39/w=3w=

We move all terms to the left:

39/w-(3w)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

-3w+39/w=0

We multiply all the terms by the denominator


-3w*w+39=0

Wy multiply elements

-3w^2+39=0

a = -3; b = 0; c = +39;
Δ = b2-4ac
Δ = 02-4·(-3)·39
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{13}}{2*-3}=\frac{0-6\sqrt{13}}{-6}
=-\frac{6\sqrt{13}}{-6}
=-\frac{\sqrt{13}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{13}}{2*-3}=\frac{0+6\sqrt{13}}{-6}
=\frac{6\sqrt{13}}{-6}
=\frac{\sqrt{13}}{-1}
$