X(x-1)=7x+33

Solution for X(x-1)=7x+33 equation:

X(X-1)=7X+33

We move all terms to the left:

X(X-1)-(7X+33)=0

We multiply parentheses

X^2-1X-(7X+33)=0

We get rid of parentheses

X^2-1X-7X-33=0

We add all the numbers together, and all the variables

X^2-8X-33=0

a = 1; b = -8; c = -33;
Δ = b2-4ac
Δ = -82-4·1·(-33)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-14}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+14}{2*1}=\frac{22}{2}
=11
$