2y+1=3/4y+3

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

2y+1=3/4y+3

We move all terms to the left:

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


Domain of the equation: 4y+3)!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8y^2-12y+4y-3=0

We add all the numbers together, and all the variables

8y^2-8y-3=0

a = 8; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·8·(-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{-(-8)-4\sqrt{10}}{2*8}=\frac{8-4\sqrt{10}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*8}=\frac{8+4\sqrt{10}}{16}
$