4/7w=16w

Solution for 4/7w=16w equation:

4/7w=16w

We move all terms to the left:

4/7w-(16w)=0


Domain of the equation: 7w!=0

w!=0/7

w!=0

w∈R


We add all the numbers together, and all the variables

-16w+4/7w=0

We multiply all the terms by the denominator


-16w*7w+4=0

Wy multiply elements

-112w^2+4=0

a = -112; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-112)·4
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{7}}{2*-112}=\frac{0-16\sqrt{7}}{-224}
=-\frac{16\sqrt{7}}{-224}
=-\frac{\sqrt{7}}{-14}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{7}}{2*-112}=\frac{0+16\sqrt{7}}{-224}
=\frac{16\sqrt{7}}{-224}
=\frac{\sqrt{7}}{-14}
$