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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-8x)/32x^2+(-12x)/32x^2-3+2=0

We add all the numbers together, and all the variables

(-8x)/32x^2+(-12x)/32x^2-1=0

We multiply all the terms by the denominator


(-8x)+(-12x)-1*32x^2=0

Wy multiply elements

-32x^2+(-8x)+(-12x)=0

We get rid of parentheses

-32x^2-8x-12x=0

We add all the numbers together, and all the variables

-32x^2-20x=0

a = -32; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-32)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-32}=\frac{40}{-64}
=-5/8
$