4/6y+1/2y-3=12

Solution for 4/6y+1/2y-3=12 equation:

4/6y+1/2y-3=12

We move all terms to the left:

4/6y+1/2y-3-(12)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

4/6y+1/2y-15=0

We calculate fractions


8y/12y^2+6y/12y^2-15=0

We multiply all the terms by the denominator


8y+6y-15*12y^2=0

We add all the numbers together, and all the variables

14y-15*12y^2=0

Wy multiply elements

-180y^2+14y=0

a = -180; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-180)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-180}=\frac{-28}{-360}
=7/90
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-180}=\frac{0}{-360}
=0
$