3/4y-2=2y+1

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

3/4y-2=2y+1

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -8; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·(-8)·3
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*-8}=\frac{12-4\sqrt{15}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*-8}=\frac{12+4\sqrt{15}}{-16}
$