(2x-1)(10x+1)=0

Solution for (2x-1)(10x+1)=0 equation:

(2x-1)(10x+1)=0

We multiply parentheses ..

(+20x^2+2x-10x-1)=0

We get rid of parentheses

20x^2+2x-10x-1=0

We add all the numbers together, and all the variables

20x^2-8x-1=0

a = 20; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·20·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*20}=\frac{-4}{40}
=-1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*20}=\frac{20}{40}
=1/2
$