(X)(x-3)=154

Solution for (X)(x-3)=154 equation:

(X)(X-3)=154

We move all terms to the left:

(X)(X-3)-(154)=0

We multiply parentheses

X^2-3X-154=0

a = 1; b = -3; c = -154;
Δ = b2-4ac
Δ = -32-4·1·(-154)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-25}{2*1}=\frac{-22}{2}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+25}{2*1}=\frac{28}{2}
=14
$