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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


(-384x^2)/360x^2+320x^2/360x^2+180x/360x^2+270x/360x^2=0

We multiply all the terms by the denominator


(-384x^2)+320x^2+180x+270x=0

We add all the numbers together, and all the variables

320x^2+(-384x^2)+450x=0

We get rid of parentheses

320x^2-384x^2+450x=0

We add all the numbers together, and all the variables

-64x^2+450x=0

a = -64; b = 450; c = 0;
Δ = b2-4ac
Δ = 4502-4·(-64)·0
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-450}{2*-64}=\frac{-900}{-128}
=7+1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+450}{2*-64}=\frac{0}{-128}
=0
$