X^2+3x-1/9=0

Solution for X^2+3x-1/9=0 equation:

X^2+3X-1/9=0

We multiply all the terms by the denominator


X^2*9+3X*9-1=0

Wy multiply elements

9X^2+27X-1=0

a = 9; b = 27; c = -1;
Δ = b2-4ac
Δ = 272-4·9·(-1)
Δ = 765
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:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{85}}{2*9}=\frac{-27-3\sqrt{85}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{85}}{2*9}=\frac{-27+3\sqrt{85}}{18}
$