1.5=3x-15/x

Solution for 1.5=3x-15/x equation:

1.5=3x-15/x

We move all terms to the left:

1.5-(3x-15/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+3x-15/x)+1.5=0

We get rid of parentheses

-3x+15/x+1.5=0

We multiply all the terms by the denominator


-3x*x+(1.5)*x+15=0

We multiply parentheses

-3x*x+1.5x+15=0

Wy multiply elements

-3x^2+1.5x+15=0

a = -3; b = 1.5; c = +15;
Δ = b2-4ac
Δ = 1.52-4·(-3)·15
Δ = 182.25
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{-(1.5)-\sqrt{182.25}}{2*-3}=\frac{-1.5-\sqrt{182.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{182.25}}{2*-3}=\frac{-1.5+\sqrt{182.25}}{-6}
$