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

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

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

We multiply parentheses ..

(+30x^2+6x-25x-5)=0

We get rid of parentheses

30x^2+6x-25x-5=0

We add all the numbers together, and all the variables

30x^2-19x-5=0

a = 30; b = -19; c = -5;
Δ = b2-4ac
Δ = -192-4·30·(-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{-(-19)-31}{2*30}=\frac{-12}{60}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+31}{2*30}=\frac{50}{60}
=5/6
$