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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


(-160x^2)/512x^2+256x/512x^2+384x/512x^2=0

We multiply all the terms by the denominator


(-160x^2)+256x+384x=0

We add all the numbers together, and all the variables

(-160x^2)+640x=0

We get rid of parentheses

-160x^2+640x=0

a = -160; b = 640; c = 0;
Δ = b2-4ac
Δ = 6402-4·(-160)·0
Δ = 409600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{409600}=640$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-640}{2*-160}=\frac{-1280}{-320}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+640}{2*-160}=\frac{0}{-320}
=0
$