(-3x-1)(x-9)=0

Solution for (-3x-1)(x-9)=0 equation:

(-3x-1)(x-9)=0

We multiply parentheses ..

(-3x^2+27x-1x+9)=0

We get rid of parentheses

-3x^2+27x-1x+9=0

We add all the numbers together, and all the variables

-3x^2+26x+9=0

a = -3; b = 26; c = +9;
Δ = b2-4ac
Δ = 262-4·(-3)·9
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-28}{2*-3}=\frac{-54}{-6}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+28}{2*-3}=\frac{2}{-6}
=-1/3
$