1.5x-1080/x=9

Solution for 1.5x-1080/x=9 equation:

1.5x-1080/x=9

We move all terms to the left:

1.5x-1080/x-(9)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


(1.5x)*x-9*x-1080=0

We add all the numbers together, and all the variables

(+1.5x)*x-9*x-1080=0

We add all the numbers together, and all the variables

-9x+(+1.5x)*x-1080=0

We multiply parentheses

x^2-9x-1080=0

a = 1; b = -9; c = -1080;
Δ = b2-4ac
Δ = -92-4·1·(-1080)
Δ = 4401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4401}=\sqrt{9*489}=\sqrt{9}*\sqrt{489}=3\sqrt{489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{489}}{2*1}=\frac{9-3\sqrt{489}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{489}}{2*1}=\frac{9+3\sqrt{489}}{2}
$