2y-1=3/4y=9

Solution for 2y-1=3/4y=9 equation:

2y-1=3/4y=9

We move all terms to the left:

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


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2y-3/4y-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

8y^2-4y-3=0

a = 8; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·8·(-3)
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{-(-4)-4\sqrt{7}}{2*8}=\frac{4-4\sqrt{7}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*8}=\frac{4+4\sqrt{7}}{16}
$