X(x-3)=152

Solution for X(x-3)=152 equation:

X(X-3)=152

We move all terms to the left:

X(X-3)-(152)=0

We multiply parentheses

X^2-3X-152=0

a = 1; b = -3; c = -152;
Δ = b2-4ac
Δ = -32-4·1·(-152)
Δ = 617
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{617}}{2*1}=\frac{3-\sqrt{617}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{617}}{2*1}=\frac{3+\sqrt{617}}{2}
$