X(x-3)/2=60

Solution for X(x-3)/2=60 equation:

X(X-3)/2=60

We move all terms to the left:

X(X-3)/2-(60)=0

We multiply all the terms by the denominator


X(X-3)-60*2=0

We add all the numbers together, and all the variables

X(X-3)-120=0

We multiply parentheses

X^2-3X-120=0

a = 1; b = -3; c = -120;
Δ = b2-4ac
Δ = -32-4·1·(-120)
Δ = 489
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{-(-3)-\sqrt{489}}{2*1}=\frac{3-\sqrt{489}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{489}}{2*1}=\frac{3+\sqrt{489}}{2}
$