3y=3/4y-1

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

3y=3/4y-1

We move all terms to the left:

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


Domain of the equation: 4y-1)!=0

y∈R


We get rid of parentheses

3y-3/4y+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

12y^2+4y-3=0

a = 12; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·12·(-3)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*12}=\frac{-4-4\sqrt{10}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*12}=\frac{-4+4\sqrt{10}}{24}
$