x(x-7)=3

Solution for x(x-7)=3 equation:

x(x-7)=3

We move all terms to the left:

x(x-7)-(3)=0

We multiply parentheses

x^2-7x-3=0

a = 1; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·1·(-3)
Δ = 61
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{61}}{2*1}=\frac{7-\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*1}=\frac{7+\sqrt{61}}{2}
$