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

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

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

We move all terms to the left:

1/4x+3/8-(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

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

We get rid of parentheses

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

We calculate fractions


144x^2/3072x^2+768x/3072x^2+(-1792x)/3072x^2-3=0

We multiply all the terms by the denominator


144x^2+768x+(-1792x)-3*3072x^2=0

Wy multiply elements

144x^2-9216x^2+768x+(-1792x)=0

We get rid of parentheses

144x^2-9216x^2+768x-1792x=0

We add all the numbers together, and all the variables

-9072x^2-1024x=0

a = -9072; b = -1024; c = 0;
Δ = b2-4ac
Δ = -10242-4·(-9072)·0
Δ = 1048576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1048576}=1024$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1024)-1024}{2*-9072}=\frac{0}{-18144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1024)+1024}{2*-9072}=\frac{2048}{-18144}
=-64/567
$