(4x+5)(4x-1)=0

Solution for (4x+5)(4x-1)=0 equation:

(4x+5)(4x-1)=0

We multiply parentheses ..

(+16x^2-4x+20x-5)=0

We get rid of parentheses

16x^2-4x+20x-5=0

We add all the numbers together, and all the variables

16x^2+16x-5=0

a = 16; b = 16; c = -5;
Δ = b2-4ac
Δ = 162-4·16·(-5)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-24}{2*16}=\frac{-40}{32}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+24}{2*16}=\frac{8}{32}
=1/4
$