X(x+51)=204

Solution for X(x+51)=204 equation:

X(X+51)=204

We move all terms to the left:

X(X+51)-(204)=0

We multiply parentheses

X^2+51X-204=0

a = 1; b = 51; c = -204;
Δ = b2-4ac
Δ = 512-4·1·(-204)
Δ = 3417
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{-(51)-\sqrt{3417}}{2*1}=\frac{-51-\sqrt{3417}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{3417}}{2*1}=\frac{-51+\sqrt{3417}}{2}
$