9x-5/6x=3

Solution for 9x-5/6x=3 equation:

9x-5/6x=3

We move all terms to the left:

9x-5/6x-(3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


9x*6x-3*6x-5=0

Wy multiply elements

54x^2-18x-5=0

a = 54; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·54·(-5)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{39}}{2*54}=\frac{18-6\sqrt{39}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{39}}{2*54}=\frac{18+6\sqrt{39}}{108}
$