3/4y+3/12y-3=-5

Solution for 3/4y+3/12y-3=-5 equation:

3/4y+3/12y-3=-5

We move all terms to the left:

3/4y+3/12y-3-(-5)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 12y!=0

y!=0/12

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y+3/12y+2=0

We calculate fractions


36y/48y^2+12y/48y^2+2=0

We multiply all the terms by the denominator


36y+12y+2*48y^2=0

We add all the numbers together, and all the variables

48y+2*48y^2=0

Wy multiply elements

96y^2+48y=0

a = 96; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·96·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*96}=\frac{-96}{192}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*96}=\frac{0}{192}
=0
$