4/1x+2=3/8x-4

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

4/1x+2=3/8x-4

We move all terms to the left:

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


Domain of the equation: 1x!=0

x∈R



Domain of the equation: 8x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

32x/8x^2+(-3x)/8x^2+6=0

We multiply all the terms by the denominator


32x+(-3x)+6*8x^2=0

Wy multiply elements

48x^2+32x+(-3x)=0

We get rid of parentheses

48x^2+32x-3x=0

We add all the numbers together, and all the variables

48x^2+29x=0

a = 48; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·48·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*48}=\frac{-58}{96}
=-29/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*48}=\frac{0}{96}
=0
$