-27/x+0.5x+1.5=0

Solution for -27/x+0.5x+1.5=0 equation:

-27/x+0.5x+1.5=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

0.5x-27/x+1.5=0

We multiply all the terms by the denominator


(0.5x)*x+(1.5)*x-27=0

We add all the numbers together, and all the variables

(+0.5x)*x+(1.5)*x-27=0

We multiply parentheses

0x^2+1.5x-27=0

We add all the numbers together, and all the variables

x^2+1.5x-27=0

a = 1; b = 1.5; c = -27;
Δ = b2-4ac
Δ = 1.52-4·1·(-27)
Δ = 110.25
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{110.25}}{2*1}=\frac{-1.5-\sqrt{110.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{110.25}}{2*1}=\frac{-1.5+\sqrt{110.25}}{2}
$