7x(x+2)=7

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

7x(x+2)=7

We move all terms to the left:

7x(x+2)-(7)=0

We multiply parentheses

7x^2+14x-7=0

a = 7; b = 14; c = -7;
Δ = b2-4ac
Δ = 142-4·7·(-7)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14\sqrt{2}}{2*7}=\frac{-14-14\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14\sqrt{2}}{2*7}=\frac{-14+14\sqrt{2}}{14}
$