5/4x+3/8=2+1/12x

Solution for 5/4x+3/8=2+1/12x equation:

5/4x+3/8=2+1/12x

We move all terms to the left:

5/4x+3/8-(2+1/12x)=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-(1/12x+2)+3/8=0

We get rid of parentheses

5/4x-1/12x-2+3/8=0

We calculate fractions


144x^2/3072x^2+3840x/3072x^2+(-256x)/3072x^2-2=0

We multiply all the terms by the denominator


144x^2+3840x+(-256x)-2*3072x^2=0

Wy multiply elements

144x^2-6144x^2+3840x+(-256x)=0

We get rid of parentheses

144x^2-6144x^2+3840x-256x=0

We add all the numbers together, and all the variables

-6000x^2+3584x=0

a = -6000; b = 3584; c = 0;
Δ = b2-4ac
Δ = 35842-4·(-6000)·0
Δ = 12845056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12845056}=3584$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3584)-3584}{2*-6000}=\frac{-7168}{-12000}
=224/375
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3584)+3584}{2*-6000}=\frac{0}{-12000}
=0
$