5w-16/w=6

Solution for 5w-16/w=6 equation:

5w-16/w=6

We move all terms to the left:

5w-16/w-(6)=0


Domain of the equation: w!=0

w∈R


We multiply all the terms by the denominator


5w*w-6*w-16=0

We add all the numbers together, and all the variables

-6w+5w*w-16=0

Wy multiply elements

5w^2-6w-16=0

a = 5; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·5·(-16)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{89}}{2*5}=\frac{6-2\sqrt{89}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{89}}{2*5}=\frac{6+2\sqrt{89}}{10}
$