32-3/8x=3/4x+5

Solution for 32-3/8x=3/4x+5 equation:

32-3/8x=3/4x+5

We move all terms to the left:

32-3/8x-(3/4x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

-3/8x-3/4x-5+32=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-12x)/32x^2+(-24x)/32x^2+27=0

We multiply all the terms by the denominator


(-12x)+(-24x)+27*32x^2=0

Wy multiply elements

864x^2+(-12x)+(-24x)=0

We get rid of parentheses

864x^2-12x-24x=0

We add all the numbers together, and all the variables

864x^2-36x=0

a = 864; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·864·0
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*864}=\frac{0}{1728}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*864}=\frac{72}{1728}
=1/24
$