(X+9)(x+6)=306

Solution for (X+9)(x+6)=306 equation:

(X+9)(X+6)=306

We move all terms to the left:

(X+9)(X+6)-(306)=0

We multiply parentheses ..

(+X^2+6X+9X+54)-306=0

We get rid of parentheses

X^2+6X+9X+54-306=0

We add all the numbers together, and all the variables

X^2+15X-252=0

a = 1; b = 15; c = -252;
Δ = b2-4ac
Δ = 152-4·1·(-252)
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{137}}{2*1}=\frac{-15-3\sqrt{137}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{137}}{2*1}=\frac{-15+3\sqrt{137}}{2}
$