1/4x-3/2x=11/8

Solution for 1/4x-3/2x=11/8 equation:

1/4x-3/2x=11/8

We move all terms to the left:

1/4x-3/2x-(11/8)=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-3/2x-(+11/8)=0

We get rid of parentheses

1/4x-3/2x-11/8=0

We calculate fractions


(-176x^2)/512x^2+128x/512x^2+(-768x)/512x^2=0

We multiply all the terms by the denominator


(-176x^2)+128x+(-768x)=0

We get rid of parentheses

-176x^2+128x-768x=0

We add all the numbers together, and all the variables

-176x^2-640x=0

a = -176; b = -640; c = 0;
Δ = b2-4ac
Δ = -6402-4·(-176)·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*-176}=\frac{0}{-352}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-640)+640}{2*-176}=\frac{1280}{-352}
=-3+7/11
$