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

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

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

We multiply parentheses ..

(+6x^2+x-36x-6)=0

We get rid of parentheses

6x^2+x-36x-6=0

We add all the numbers together, and all the variables

6x^2-35x-6=0

a = 6; b = -35; c = -6;
Δ = b2-4ac
Δ = -352-4·6·(-6)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-37}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+37}{2*6}=\frac{72}{12}
=6
$