3/8x-4=1/4x+6

Solution for 3/8x-4=1/4x+6 equation:

3/8x-4=1/4x+6

We move all terms to the left:

3/8x-4-(1/4x+6)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

3/8x-1/4x-6-4=0

We calculate fractions


12x/32x^2+(-8x)/32x^2-6-4=0

We add all the numbers together, and all the variables

12x/32x^2+(-8x)/32x^2-10=0

We multiply all the terms by the denominator


12x+(-8x)-10*32x^2=0

Wy multiply elements

-320x^2+12x+(-8x)=0

We get rid of parentheses

-320x^2+12x-8x=0

We add all the numbers together, and all the variables

-320x^2+4x=0

a = -320; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-320)·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*-320}=\frac{-8}{-640}
=1/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-320}=\frac{0}{-640}
=0
$