y-5/6y=19

Solution for y-5/6y=19 equation:

y-5/6y=19

We move all terms to the left:

y-5/6y-(19)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We multiply all the terms by the denominator


y*6y-19*6y-5=0

Wy multiply elements

6y^2-114y-5=0

a = 6; b = -114; c = -5;
Δ = b2-4ac
Δ = -1142-4·6·(-5)
Δ = 13116
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:

$\sqrt{\Delta}=\sqrt{13116}=\sqrt{4*3279}=\sqrt{4}*\sqrt{3279}=2\sqrt{3279}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{3279}}{2*6}=\frac{114-2\sqrt{3279}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{3279}}{2*6}=\frac{114+2\sqrt{3279}}{12}
$