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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

8x/32x^2+(-12x)/32x^2-11=0

We multiply all the terms by the denominator


8x+(-12x)-11*32x^2=0

Wy multiply elements

-352x^2+8x+(-12x)=0

We get rid of parentheses

-352x^2+8x-12x=0

We add all the numbers together, and all the variables

-352x^2-4x=0

a = -352; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-352)·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*-352}=\frac{0}{-704}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-352}=\frac{8}{-704}
=-1/88
$