X(x+6)=154

Solution for X(x+6)=154 equation:

X(X+6)=154

We move all terms to the left:

X(X+6)-(154)=0

We multiply parentheses

X^2+6X-154=0

a = 1; b = 6; c = -154;
Δ = b2-4ac
Δ = 62-4·1·(-154)
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{163}}{2*1}=\frac{-6-2\sqrt{163}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{163}}{2*1}=\frac{-6+2\sqrt{163}}{2}
$