4x(4x-1)=16

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

4x(4x-1)=16

We move all terms to the left:

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

We multiply parentheses

16x^2-4x-16=0

a = 16; b = -4; c = -16;
Δ = b2-4ac
Δ = -42-4·16·(-16)
Δ = 1040
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{65}}{2*16}=\frac{4-4\sqrt{65}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{65}}{2*16}=\frac{4+4\sqrt{65}}{32}
$