6x-5=7/9x

Solution for 6x-5=7/9x equation:

6x-5=7/9x

We move all terms to the left:

6x-5-(7/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+7/9x)-5=0

We get rid of parentheses

6x-7/9x-5=0

We multiply all the terms by the denominator


6x*9x-5*9x-7=0

Wy multiply elements

54x^2-45x-7=0

a = 54; b = -45; c = -7;
Δ = b2-4ac
Δ = -452-4·54·(-7)
Δ = 3537
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:

$\sqrt{\Delta}=\sqrt{3537}=\sqrt{9*393}=\sqrt{9}*\sqrt{393}=3\sqrt{393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{393}}{2*54}=\frac{45-3\sqrt{393}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{393}}{2*54}=\frac{45+3\sqrt{393}}{108}
$