56x(2+2x)=1

Solution for 56x(2+2x)=1 equation:

56x(2+2x)=1

We move all terms to the left:

56x(2+2x)-(1)=0

We add all the numbers together, and all the variables

56x(2x+2)-1=0

We multiply parentheses

112x^2+112x-1=0

a = 112; b = 112; c = -1;
Δ = b2-4ac
Δ = 1122-4·112·(-1)
Δ = 12992
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:

$\sqrt{\Delta}=\sqrt{12992}=\sqrt{64*203}=\sqrt{64}*\sqrt{203}=8\sqrt{203}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-8\sqrt{203}}{2*112}=\frac{-112-8\sqrt{203}}{224}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+8\sqrt{203}}{2*112}=\frac{-112+8\sqrt{203}}{224}
$