X(7x+2)=1

Solution for X(7x+2)=1 equation:

X(7X+2)=1

We move all terms to the left:

X(7X+2)-(1)=0

We multiply parentheses

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}
$