(9x-11)(3x+16)=0

Solution for (9x-11)(3x+16)=0 equation:

(9x-11)(3x+16)=0

We multiply parentheses ..

(+27x^2+144x-33x-176)=0

We get rid of parentheses

27x^2+144x-33x-176=0

We add all the numbers together, and all the variables

27x^2+111x-176=0

a = 27; b = 111; c = -176;
Δ = b2-4ac
Δ = 1112-4·27·(-176)
Δ = 31329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{31329}=177$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-177}{2*27}=\frac{-288}{54}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+177}{2*27}=\frac{66}{54}
=1+2/9
$