y-5/6y+2=10

Solution for y-5/6y+2=10 equation:

y-5/6y+2=10

We move all terms to the left:

y-5/6y+2-(10)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

y-5/6y-8=0

We multiply all the terms by the denominator


y*6y-8*6y-5=0

Wy multiply elements

6y^2-48y-5=0

a = 6; b = -48; c = -5;
Δ = b2-4ac
Δ = -482-4·6·(-5)
Δ = 2424
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:

$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{606}}{2*6}=\frac{48-2\sqrt{606}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{606}}{2*6}=\frac{48+2\sqrt{606}}{12}
$