3/8x-4.5x=0.4

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Solution for 3/8x-4.5x=0.4 equation: 



3/8x-4.5x=0.4

We move all terms to the left:

3/8x-4.5x-(0.4)=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-0.4=0

We multiply all the terms by the denominator


-(4.5x)*8x-(0.4)*8x+3=0

We add all the numbers together, and all the variables

-(+4.5x)*8x-(0.4)*8x+3=0

We multiply parentheses

-32x^2-3.2x+3=0

a = -32; b = -3.2; c = +3;
Δ = b2-4ac
Δ = -3.22-4·(-32)·3
Δ = 394.24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3.2)-\sqrt{394.24}}{2*-32}=\frac{3.2-\sqrt{394.24}}{-64}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.2)+\sqrt{394.24}}{2*-32}=\frac{3.2+\sqrt{394.24}}{-64}
$

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