2/3x+3/4x=7/8

Solution for 2/3x+3/4x=7/8 equation:

2/3x+3/4x=7/8

We move all terms to the left:

2/3x+3/4x-(7/8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+3/4x-(+7/8)=0

We get rid of parentheses

2/3x+3/4x-7/8=0

We calculate fractions


(-336x^2)/768x^2+512x/768x^2+576x/768x^2=0

We multiply all the terms by the denominator


(-336x^2)+512x+576x=0

We add all the numbers together, and all the variables

(-336x^2)+1088x=0

We get rid of parentheses

-336x^2+1088x=0

a = -336; b = 1088; c = 0;
Δ = b2-4ac
Δ = 10882-4·(-336)·0
Δ = 1183744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1183744}=1088$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1088)-1088}{2*-336}=\frac{-2176}{-672}
=3+5/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1088)+1088}{2*-336}=\frac{0}{-672}
=0
$