x(x-7)=33

Solution for x(x-7)=33 equation:

x(x-7)=33

We move all terms to the left:

x(x-7)-(33)=0

We multiply parentheses

x^2-7x-33=0

a = 1; b = -7; c = -33;
Δ = b2-4ac
Δ = -72-4·1·(-33)
Δ = 181
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{181}}{2*1}=\frac{7-\sqrt{181}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{181}}{2*1}=\frac{7+\sqrt{181}}{2}
$