X(x-6)=187

Solution for X(x-6)=187 equation:

X(X-6)=187

We move all terms to the left:

X(X-6)-(187)=0

We multiply parentheses

X^2-6X-187=0

a = 1; b = -6; c = -187;
Δ = b2-4ac
Δ = -62-4·1·(-187)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-28}{2*1}=\frac{-22}{2}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+28}{2*1}=\frac{34}{2}
=17
$