3/4x-2/3x+5/8=1

Solution for 3/4x-2/3x+5/8=1 equation:

3/4x-2/3x+5/8=1

We move all terms to the left:

3/4x-2/3x+5/8-(1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


determiningTheFunctionDomain
3/4x-2/3x-1+5/8=0

We calculate fractions


180x^2/768x^2+576x/768x^2+(-512x)/768x^2-1=0

We multiply all the terms by the denominator


180x^2+576x+(-512x)-1*768x^2=0

Wy multiply elements

180x^2-768x^2+576x+(-512x)=0

We get rid of parentheses

180x^2-768x^2+576x-512x=0

We add all the numbers together, and all the variables

-588x^2+64x=0

a = -588; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-588)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-588}=\frac{-128}{-1176}
=16/147
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-588}=\frac{0}{-1176}
=0
$