(6x-1)(x+5)=0

Solution for (6x-1)(x+5)=0 equation:

(6x-1)(x+5)=0

We multiply parentheses ..

(+6x^2+30x-1x-5)=0

We get rid of parentheses

6x^2+30x-1x-5=0

We add all the numbers together, and all the variables

6x^2+29x-5=0

a = 6; b = 29; c = -5;
Δ = b2-4ac
Δ = 292-4·6·(-5)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-31}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+31}{2*6}=\frac{2}{12}
=1/6
$