X(x-5)=48

Solution for X(x-5)=48 equation:

X(X-5)=48

We move all terms to the left:

X(X-5)-(48)=0

We multiply parentheses

X^2-5X-48=0

a = 1; b = -5; c = -48;
Δ = b2-4ac
Δ = -52-4·1·(-48)
Δ = 217
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{-(-5)-\sqrt{217}}{2*1}=\frac{5-\sqrt{217}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*1}=\frac{5+\sqrt{217}}{2}
$