x(x+7)=1

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

x(x+7)=1

We move all terms to the left:

x(x+7)-(1)=0

We multiply parentheses

x^2+7x-1=0

a = 1; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·1·(-1)
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{53}}{2*1}=\frac{-7-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{53}}{2*1}=\frac{-7+\sqrt{53}}{2}
$