x*(x-7)=13

Solution for x*(x-7)=13 equation:

x(x-7)=13

We move all terms to the left:

x(x-7)-(13)=0

We multiply parentheses

x^2-7x-13=0

a = 1; b = -7; c = -13;
Δ = b2-4ac
Δ = -72-4·1·(-13)
Δ = 101
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{101}}{2*1}=\frac{7-\sqrt{101}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{101}}{2*1}=\frac{7+\sqrt{101}}{2}
$