7x^2-2x=1

Solution for 7x^2-2x=1 equation:

7x^2-2x=1

We move all terms to the left:

7x^2-2x-(1)=0

a = 7; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·7·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{2}}{2*7}=\frac{2-4\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{2}}{2*7}=\frac{2+4\sqrt{2}}{14}
$