3/8x-4.5x=0.5

Solution for 3/8x-4.5x=0.5 equation:

3/8x-4.5x=0.5

We move all terms to the left:

3/8x-4.5x-(0.5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-4.5x+3/8x-0.5=0

We multiply all the terms by the denominator


-(4.5x)*8x-(0.5)*8x+3=0

We add all the numbers together, and all the variables

-(+4.5x)*8x-(0.5)*8x+3=0

We multiply parentheses

-32x^2-4x+3=0

a = -32; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-32)·3
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{-(-4)-20}{2*-32}=\frac{-16}{-64}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*-32}=\frac{24}{-64}
=-3/8
$