13-3/4x=3/8x-5

Solution for 13-3/4x=3/8x-5 equation:

13-3/4x=3/8x-5

We move all terms to the left:

13-3/4x-(3/8x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-5)!=0

x∈R


We get rid of parentheses

-3/4x-3/8x+5+13=0

We calculate fractions


(-24x)/32x^2+(-12x)/32x^2+5+13=0

We add all the numbers together, and all the variables

(-24x)/32x^2+(-12x)/32x^2+18=0

We multiply all the terms by the denominator


(-24x)+(-12x)+18*32x^2=0

Wy multiply elements

576x^2+(-24x)+(-12x)=0

We get rid of parentheses

576x^2-24x-12x=0

We add all the numbers together, and all the variables

576x^2-36x=0

a = 576; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·576·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*576}=\frac{0}{1152}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*576}=\frac{72}{1152}
=1/16
$