9x-4/3x=6

Solution for 9x-4/3x=6 equation:

9x-4/3x=6

We move all terms to the left:

9x-4/3x-(6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


9x*3x-6*3x-4=0

Wy multiply elements

27x^2-18x-4=0

a = 27; b = -18; c = -4;
Δ = b2-4ac
Δ = -182-4·27·(-4)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{21}}{2*27}=\frac{18-6\sqrt{21}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{21}}{2*27}=\frac{18+6\sqrt{21}}{54}
$