19w+1/8w=39

Solution for 19w+1/8w=39 equation:

19w+1/8w=39

We move all terms to the left:

19w+1/8w-(39)=0


Domain of the equation: 8w!=0

w!=0/8

w!=0

w∈R


We multiply all the terms by the denominator


19w*8w-39*8w+1=0

Wy multiply elements

152w^2-312w+1=0

a = 152; b = -312; c = +1;
Δ = b2-4ac
Δ = -3122-4·152·1
Δ = 96736
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:

$\sqrt{\Delta}=\sqrt{96736}=\sqrt{16*6046}=\sqrt{16}*\sqrt{6046}=4\sqrt{6046}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-312)-4\sqrt{6046}}{2*152}=\frac{312-4\sqrt{6046}}{304}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-312)+4\sqrt{6046}}{2*152}=\frac{312+4\sqrt{6046}}{304}
$