(6x-1)(x+9)=0

Solution for (6x-1)(x+9)=0 equation:

(6x-1)(x+9)=0

We multiply parentheses ..

(+6x^2+54x-1x-9)=0

We get rid of parentheses

6x^2+54x-1x-9=0

We add all the numbers together, and all the variables

6x^2+53x-9=0

a = 6; b = 53; c = -9;
Δ = b2-4ac
Δ = 532-4·6·(-9)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-55}{2*6}=\frac{-108}{12}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+55}{2*6}=\frac{2}{12}
=1/6
$