2y-6/4y-8=1

Solution for 2y-6/4y-8=1 equation:

2y-6/4y-8=1

We move all terms to the left:

2y-6/4y-8-(1)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

2y-6/4y-9=0

We multiply all the terms by the denominator


2y*4y-9*4y-6=0

Wy multiply elements

8y^2-36y-6=0

a = 8; b = -36; c = -6;
Δ = b2-4ac
Δ = -362-4·8·(-6)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{93}}{2*8}=\frac{36-4\sqrt{93}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{93}}{2*8}=\frac{36+4\sqrt{93}}{16}
$