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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/32x^2+(-8x)/32x^2-3-4=0

We add all the numbers together, and all the variables

12x/32x^2+(-8x)/32x^2-7=0

We multiply all the terms by the denominator


12x+(-8x)-7*32x^2=0

Wy multiply elements

-224x^2+12x+(-8x)=0

We get rid of parentheses

-224x^2+12x-8x=0

We add all the numbers together, and all the variables

-224x^2+4x=0

a = -224; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-224)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-224}=\frac{-8}{-448}
=1/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-224}=\frac{0}{-448}
=0
$