X(x+12)=50

Solution for X(x+12)=50 equation:

X(X+12)=50

We move all terms to the left:

X(X+12)-(50)=0

We multiply parentheses

X^2+12X-50=0

a = 1; b = 12; c = -50;
Δ = b2-4ac
Δ = 122-4·1·(-50)
Δ = 344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{86}}{2*1}=\frac{-12-2\sqrt{86}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{86}}{2*1}=\frac{-12+2\sqrt{86}}{2}
$