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

Solution for (5x-9)=5/3x- equation:

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

We move all terms to the left:

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


Domain of the equation: 3x-)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5x-5/3x-9=0

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2-27x-5=0

a = 15; b = -27; c = -5;
Δ = b2-4ac
Δ = -272-4·15·(-5)
Δ = 1029
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:

$\sqrt{\Delta}=\sqrt{1029}=\sqrt{49*21}=\sqrt{49}*\sqrt{21}=7\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-7\sqrt{21}}{2*15}=\frac{27-7\sqrt{21}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+7\sqrt{21}}{2*15}=\frac{27+7\sqrt{21}}{30}
$