(X)(x-3)=222.75

Solution for (X)(x-3)=222.75 equation:

(X)(X-3)=222.75

We move all terms to the left:

(X)(X-3)-(222.75)=0

We add all the numbers together, and all the variables

X(X-3)-222.75=0

We multiply parentheses

X^2-3X-222.75=0

a = 1; b = -3; c = -222.75;
Δ = b2-4ac
Δ = -32-4·1·(-222.75)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-30}{2*1}=\frac{-27}{2}
=-13+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+30}{2*1}=\frac{33}{2}
=16+1/2
$