1/x+0.4=1.5x

Solution for 1/x+0.4=1.5x equation:

1/x+0.4=1.5x

We move all terms to the left:

1/x+0.4-(1.5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/x-(+1.5x)+0.4=0

We get rid of parentheses

1/x-1.5x+0.4=0

We multiply all the terms by the denominator


-(1.5x)*x+(0.4)*x+1=0

We add all the numbers together, and all the variables

-(+1.5x)*x+(0.4)*x+1=0

We multiply parentheses

-x^2+0.4x+1=0

We add all the numbers together, and all the variables

-1x^2+0.4x+1=0

a = -1; b = 0.4; c = +1;
Δ = b2-4ac
Δ = 0.42-4·(-1)·1
Δ = 4.16
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{-(0.4)-\sqrt{4.16}}{2*-1}=\frac{-0.4-\sqrt{4.16}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.4)+\sqrt{4.16}}{2*-1}=\frac{-0.4+\sqrt{4.16}}{-2}
$