9x(3x+8)=0

Solution for 9x(3x+8)=0 equation:

9x(3x+8)=0

We multiply parentheses

27x^2+72x=0

a = 27; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·27·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*27}=\frac{-144}{54}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*27}=\frac{0}{54}
=0
$