7/8x+1/3x=1+5/3x

Solution for 7/8x+1/3x=1+5/3x equation:

7/8x+1/3x=1+5/3x

We move all terms to the left:

7/8x+1/3x-(1+5/3x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/8x+1/3x-(5/3x+1)=0

We get rid of parentheses

7/8x+1/3x-5/3x-1=0

We calculate fractions


21x/24x^2+(-40x+1)/24x^2-1=0

We multiply all the terms by the denominator


21x+(-40x+1)-1*24x^2=0

Wy multiply elements

-24x^2+21x+(-40x+1)=0

We get rid of parentheses

-24x^2+21x-40x+1=0

We add all the numbers together, and all the variables

-24x^2-19x+1=0

a = -24; b = -19; c = +1;
Δ = b2-4ac
Δ = -192-4·(-24)·1
Δ = 457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{457}}{2*-24}=\frac{19-\sqrt{457}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{457}}{2*-24}=\frac{19+\sqrt{457}}{-48}
$