2y-3/4y+2(2y-6)=14

Solution for 2y-3/4y+2(2y-6)=14 equation:

2y-3/4y+2(2y-6)=14

We move all terms to the left:

2y-3/4y+2(2y-6)-(14)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We multiply parentheses

2y-3/4y+4y-12-14=0

We multiply all the terms by the denominator


2y*4y+4y*4y-12*4y-14*4y-3=0

Wy multiply elements

8y^2+16y^2-48y-56y-3=0

We add all the numbers together, and all the variables

24y^2-104y-3=0

a = 24; b = -104; c = -3;
Δ = b2-4ac
Δ = -1042-4·24·(-3)
Δ = 11104
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:

$\sqrt{\Delta}=\sqrt{11104}=\sqrt{16*694}=\sqrt{16}*\sqrt{694}=4\sqrt{694}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{694}}{2*24}=\frac{104-4\sqrt{694}}{48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{694}}{2*24}=\frac{104+4\sqrt{694}}{48}
$