1/6y-3=4y+2

Solution for 1/6y-3=4y+2 equation:

1/6y-3=4y+2

We move all terms to the left:

1/6y-3-(4y+2)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We get rid of parentheses

1/6y-4y-2-3=0

We multiply all the terms by the denominator


-4y*6y-2*6y-3*6y+1=0

Wy multiply elements

-24y^2-12y-18y+1=0

We add all the numbers together, and all the variables

-24y^2-30y+1=0

a = -24; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-24)·1
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{249}}{2*-24}=\frac{30-2\sqrt{249}}{-48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{249}}{2*-24}=\frac{30+2\sqrt{249}}{-48}
$