16/6*w=102

Solution for 16/6*w=102 equation:

16/6*w=102

We move all terms to the left:

16/6*w-(102)=0


Domain of the equation: 6*w!=0

w!=0/1

w!=0

w∈R


We multiply all the terms by the denominator


-102*6*w+16=0

Wy multiply elements

-612w*w+16=0

Wy multiply elements

-612w^2+16=0

a = -612; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-612)·16
Δ = 39168
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:

$\sqrt{\Delta}=\sqrt{39168}=\sqrt{2304*17}=\sqrt{2304}*\sqrt{17}=48\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{17}}{2*-612}=\frac{0-48\sqrt{17}}{-1224}
=-\frac{48\sqrt{17}}{-1224}
=-\frac{2\sqrt{17}}{-51}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{17}}{2*-612}=\frac{0+48\sqrt{17}}{-1224}
=\frac{48\sqrt{17}}{-1224}
=\frac{2\sqrt{17}}{-51}
$