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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-80x^2)/512x^2+128x/512x^2+256x/512x^2=0

We multiply all the terms by the denominator


(-80x^2)+128x+256x=0

We add all the numbers together, and all the variables

(-80x^2)+384x=0

We get rid of parentheses

-80x^2+384x=0

a = -80; b = 384; c = 0;
Δ = b2-4ac
Δ = 3842-4·(-80)·0
Δ = 147456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{147456}=384$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-384}{2*-80}=\frac{-768}{-160}
=4+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+384}{2*-80}=\frac{0}{-160}
=0
$