8x^2+56x=1

Solution for 8x^2+56x=1 equation:

8x^2+56x=1

We move all terms to the left:

8x^2+56x-(1)=0

a = 8; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·8·(-1)
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-12\sqrt{22}}{2*8}=\frac{-56-12\sqrt{22}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+12\sqrt{22}}{2*8}=\frac{-56+12\sqrt{22}}{16}
$