x^2+8x+(128)/(9)=0

Solution for x^2+8x+(128)/(9)=0 equation:

x^2+8x+(128)/(9)=0

We multiply all the terms by the denominator


x^2*9+8x*9+128=0

Wy multiply elements

9x^2+72x+128=0

a = 9; b = 72; c = +128;
Δ = b2-4ac
Δ = 722-4·9·128
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24}{2*9}=\frac{-96}{18}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24}{2*9}=\frac{-48}{18}
=-2+2/3
$