y-5/6y=16

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

y-5/6y=16

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We multiply all the terms by the denominator


y*6y-16*6y-5=0

Wy multiply elements

6y^2-96y-5=0

a = 6; b = -96; c = -5;
Δ = b2-4ac
Δ = -962-4·6·(-5)
Δ = 9336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9336}=\sqrt{4*2334}=\sqrt{4}*\sqrt{2334}=2\sqrt{2334}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2334}}{2*6}=\frac{96-2\sqrt{2334}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2334}}{2*6}=\frac{96+2\sqrt{2334}}{12}
$