x^2+x-8/9=0

Solution for x^2+x-8/9=0 equation:

x^2+x-8/9=0

We multiply all the terms by the denominator


x^2*9+x*9-8=0

Wy multiply elements

9x^2+9x-8=0

a = 9; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·9·(-8)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{41}}{2*9}=\frac{-9-3\sqrt{41}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{41}}{2*9}=\frac{-9+3\sqrt{41}}{18}
$