1/3x+3/8=3/4x+16

Solution for 1/3x+3/8=3/4x+16 equation:

1/3x+3/8=3/4x+16

We move all terms to the left:

1/3x+3/8-(3/4x+16)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+16)!=0

x∈R


We get rid of parentheses

1/3x-3/4x-16+3/8=0

We calculate fractions


144x^2/768x^2+256x/768x^2+(-576x)/768x^2-16=0

We multiply all the terms by the denominator


144x^2+256x+(-576x)-16*768x^2=0

Wy multiply elements

144x^2-12288x^2+256x+(-576x)=0

We get rid of parentheses

144x^2-12288x^2+256x-576x=0

We add all the numbers together, and all the variables

-12144x^2-320x=0

a = -12144; b = -320; c = 0;
Δ = b2-4ac
Δ = -3202-4·(-12144)·0
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-320}{2*-12144}=\frac{0}{-24288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+320}{2*-12144}=\frac{640}{-24288}
=-20/759
$