2x-6/8x+2=1

Solution for 2x-6/8x+2=1 equation:

2x-6/8x+2=1

We move all terms to the left:

2x-6/8x+2-(1)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

2x-6/8x+1=0

We multiply all the terms by the denominator


2x*8x+1*8x-6=0

Wy multiply elements

16x^2+8x-6=0

a = 16; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·16·(-6)
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{7}}{2*16}=\frac{-8-8\sqrt{7}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{7}}{2*16}=\frac{-8+8\sqrt{7}}{32}
$