2(x-5)(2x+1)=0

Solution for 2(x-5)(2x+1)=0 equation:

2(x-5)(2x+1)=0

We multiply parentheses ..

2(+2x^2+x-10x-5)=0

We multiply parentheses

4x^2+2x-20x-10=0

We add all the numbers together, and all the variables

4x^2-18x-10=0

a = 4; b = -18; c = -10;
Δ = b2-4ac
Δ = -182-4·4·(-10)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-22}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+22}{2*4}=\frac{40}{8}
=5
$