y-5/6y=13

Solution for y-5/6y=13 equation:

y-5/6y=13

We move all terms to the left:

y-5/6y-(13)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We multiply all the terms by the denominator


y*6y-13*6y-5=0

Wy multiply elements

6y^2-78y-5=0

a = 6; b = -78; c = -5;
Δ = b2-4ac
Δ = -782-4·6·(-5)
Δ = 6204
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:

$\sqrt{\Delta}=\sqrt{6204}=\sqrt{4*1551}=\sqrt{4}*\sqrt{1551}=2\sqrt{1551}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1551}}{2*6}=\frac{78-2\sqrt{1551}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1551}}{2*6}=\frac{78+2\sqrt{1551}}{12}
$