2/x+1.50x=15

Solution for 2/x+1.50x=15 equation:

2/x+1.50x=15

We move all terms to the left:

2/x+1.50x-(15)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1.50x+2/x-15=0

We multiply all the terms by the denominator


(1.50x)*x-15*x+2=0

We add all the numbers together, and all the variables

(+1.50x)*x-15*x+2=0

We add all the numbers together, and all the variables

-15x+(+1.50x)*x+2=0

We multiply parentheses

x^2-15x+2=0

a = 1; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·1·2
Δ = 217
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{-(-15)-\sqrt{217}}{2*1}=\frac{15-\sqrt{217}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{217}}{2*1}=\frac{15+\sqrt{217}}{2}
$