(4x-16)(4x-1)=0

Solution for (4x-16)(4x-1)=0 equation:

(4x-16)(4x-1)=0

We multiply parentheses ..

(+16x^2-4x-64x+16)=0

We get rid of parentheses

16x^2-4x-64x+16=0

We add all the numbers together, and all the variables

16x^2-68x+16=0

a = 16; b = -68; c = +16;
Δ = b2-4ac
Δ = -682-4·16·16
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-60}{2*16}=\frac{8}{32}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+60}{2*16}=\frac{128}{32}
=4
$