7/12x+3=4/8x-1

Solution for 7/12x+3=4/8x-1 equation:

7/12x+3=4/8x-1

We move all terms to the left:

7/12x+3-(4/8x-1)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 8x-1)!=0

x∈R


We get rid of parentheses

7/12x-4/8x+1+3=0

We calculate fractions


56x/96x^2+(-48x)/96x^2+1+3=0

We add all the numbers together, and all the variables

56x/96x^2+(-48x)/96x^2+4=0

We multiply all the terms by the denominator


56x+(-48x)+4*96x^2=0

Wy multiply elements

384x^2+56x+(-48x)=0

We get rid of parentheses

384x^2+56x-48x=0

We add all the numbers together, and all the variables

384x^2+8x=0

a = 384; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·384·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*384}=\frac{-16}{768}
=-1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*384}=\frac{0}{768}
=0
$