13w-2/3w=16

Solution for 13w-2/3w=16 equation:

13w-2/3w=16

We move all terms to the left:

13w-2/3w-(16)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We multiply all the terms by the denominator


13w*3w-16*3w-2=0

Wy multiply elements

39w^2-48w-2=0

a = 39; b = -48; c = -2;
Δ = b2-4ac
Δ = -482-4·39·(-2)
Δ = 2616
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:

$\sqrt{\Delta}=\sqrt{2616}=\sqrt{4*654}=\sqrt{4}*\sqrt{654}=2\sqrt{654}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{654}}{2*39}=\frac{48-2\sqrt{654}}{78}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{654}}{2*39}=\frac{48+2\sqrt{654}}{78}
$