X*(x+6)=150

Solution for X*(x+6)=150 equation:

X(X+6)=150

We move all terms to the left:

X(X+6)-(150)=0

We multiply parentheses

X^2+6X-150=0

a = 1; b = 6; c = -150;
Δ = b2-4ac
Δ = 62-4·1·(-150)
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{159}}{2*1}=\frac{-6-2\sqrt{159}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{159}}{2*1}=\frac{-6+2\sqrt{159}}{2}
$