4(4x-1)=2x(2x+2)

Solution for 4(4x-1)=2x(2x+2) equation:

4(4x-1)=2x(2x+2)

We move all terms to the left:

4(4x-1)-(2x(2x+2))=0

We multiply parentheses

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


We calculate terms in parentheses: -(2x(2x+2)), so:

2x(2x+2)

We multiply parentheses

4x^2+4x

Back to the equation:

-(4x^2+4x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+12x-4=0

a = -4; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·(-4)·(-4)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{5}}{2*-4}=\frac{-12-4\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{5}}{2*-4}=\frac{-12+4\sqrt{5}}{-8}
$