5/6y+1=-13y+19

Solution for 5/6y+1=-13y+19 equation:

5/6y+1=-13y+19

We move all terms to the left:

5/6y+1-(-13y+19)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We get rid of parentheses

5/6y+13y-19+1=0

We multiply all the terms by the denominator


13y*6y-19*6y+1*6y+5=0

Wy multiply elements

78y^2-114y+6y+5=0

We add all the numbers together, and all the variables

78y^2-108y+5=0

a = 78; b = -108; c = +5;
Δ = b2-4ac
Δ = -1082-4·78·5
Δ = 10104
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:

$\sqrt{\Delta}=\sqrt{10104}=\sqrt{4*2526}=\sqrt{4}*\sqrt{2526}=2\sqrt{2526}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{2526}}{2*78}=\frac{108-2\sqrt{2526}}{156}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{2526}}{2*78}=\frac{108+2\sqrt{2526}}{156}
$