5/2x-3x=9

Solution for 5/2x-3x=9 equation:

5/2x-3x=9

We move all terms to the left:

5/2x-3x-(9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+5/2x-9=0

We multiply all the terms by the denominator


-3x*2x-9*2x+5=0

Wy multiply elements

-6x^2-18x+5=0

a = -6; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·(-6)·5
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{111}}{2*-6}=\frac{18-2\sqrt{111}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{111}}{2*-6}=\frac{18+2\sqrt{111}}{-12}
$