3/x+4+0.4x+0.1=14

Solution for 3/x+4+0.4x+0.1=14 equation:

3/x+4+0.4x+0.1=14

We move all terms to the left:

3/x+4+0.4x+0.1-(14)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

0.4x+3/x-9.9=0

We multiply all the terms by the denominator


(0.4x)*x-(9.9)*x+3=0

We add all the numbers together, and all the variables

(+0.4x)*x-(9.9)*x+3=0

We multiply parentheses

0x^2-9.9x+3=0

We add all the numbers together, and all the variables

x^2-9.9x+3=0

a = 1; b = -9.9; c = +3;
Δ = b2-4ac
Δ = -9.92-4·1·3
Δ = 86.01
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{-(-9.9)-\sqrt{86.01}}{2*1}=\frac{9.9-\sqrt{86.01}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.9)+\sqrt{86.01}}{2*1}=\frac{9.9+\sqrt{86.01}}{2}
$