9x^2-6x+5/6=0

Solution for 9x^2-6x+5/6=0 equation:

9x^2-6x+5/6=0

We multiply all the terms by the denominator


9x^2*6-6x*6+5=0

Wy multiply elements

54x^2-36x+5=0

a = 54; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·54·5
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{6}}{2*54}=\frac{36-6\sqrt{6}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{6}}{2*54}=\frac{36+6\sqrt{6}}{108}
$