2/8x+1/6=-3/4x+1

Solution for 2/8x+1/6=-3/4x+1 equation:

2/8x+1/6=-3/4x+1

We move all terms to the left:

2/8x+1/6-(-3/4x+1)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

2/8x+3/4x-1+1/6=0

We calculate fractions


128x^2/1152x^2+288x/1152x^2+864x/1152x^2-1=0

We multiply all the terms by the denominator


128x^2+288x+864x-1*1152x^2=0

We add all the numbers together, and all the variables

128x^2+1152x-1*1152x^2=0

Wy multiply elements

128x^2-1152x^2+1152x=0

We add all the numbers together, and all the variables

-1024x^2+1152x=0

a = -1024; b = 1152; c = 0;
Δ = b2-4ac
Δ = 11522-4·(-1024)·0
Δ = 1327104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1327104}=1152$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1152)-1152}{2*-1024}=\frac{-2304}{-2048}
=1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1152)+1152}{2*-1024}=\frac{0}{-2048}
=0
$