5/4x+1/8=3+7/12x

Solution for 5/4x+1/8=3+7/12x equation:

5/4x+1/8=3+7/12x

We move all terms to the left:

5/4x+1/8-(3+7/12x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(7/12x+3)+1/8=0

We get rid of parentheses

5/4x-7/12x-3+1/8=0

We calculate fractions


48x^2/3072x^2+3840x/3072x^2+(-1792x)/3072x^2-3=0

We multiply all the terms by the denominator


48x^2+3840x+(-1792x)-3*3072x^2=0

Wy multiply elements

48x^2-9216x^2+3840x+(-1792x)=0

We get rid of parentheses

48x^2-9216x^2+3840x-1792x=0

We add all the numbers together, and all the variables

-9168x^2+2048x=0

a = -9168; b = 2048; c = 0;
Δ = b2-4ac
Δ = 20482-4·(-9168)·0
Δ = 4194304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4194304}=2048$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2048)-2048}{2*-9168}=\frac{-4096}{-18336}
=128/573
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2048)+2048}{2*-9168}=\frac{0}{-18336}
=0
$