X*(x+5)=204

Solution for X*(x+5)=204 equation:

X(X+5)=204

We move all terms to the left:

X(X+5)-(204)=0

We multiply parentheses

X^2+5X-204=0

a = 1; b = 5; c = -204;
Δ = b2-4ac
Δ = 52-4·1·(-204)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*1}=\frac{-34}{2}
=-17
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*1}=\frac{24}{2}
=12
$