X(x-7)=330

Solution for X(x-7)=330 equation:

X(X-7)=330

We move all terms to the left:

X(X-7)-(330)=0

We multiply parentheses

X^2-7X-330=0

a = 1; b = -7; c = -330;
Δ = b2-4ac
Δ = -72-4·1·(-330)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-37}{2*1}=\frac{-30}{2}
=-15
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+37}{2*1}=\frac{44}{2}
=22
$