(-9x+5)(-3x-13)=0

Solution for (-9x+5)(-3x-13)=0 equation:

(-9x+5)(-3x-13)=0

We multiply parentheses ..

(+27x^2+117x-15x-65)=0

We get rid of parentheses

27x^2+117x-15x-65=0

We add all the numbers together, and all the variables

27x^2+102x-65=0

a = 27; b = 102; c = -65;
Δ = b2-4ac
Δ = 1022-4·27·(-65)
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-132}{2*27}=\frac{-234}{54}
=-4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+132}{2*27}=\frac{30}{54}
=5/9
$