3y-1/4y=-2

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

3y-1/4y=-2

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

3y-1/4y+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

12y^2+8y-1=0

a = 12; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·12·(-1)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*12}=\frac{-8-4\sqrt{7}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*12}=\frac{-8+4\sqrt{7}}{24}
$