(2x+3)(x+9)=360

Solution for (2x+3)(x+9)=360 equation:

(2x+3)(x+9)=360

We move all terms to the left:

(2x+3)(x+9)-(360)=0

We multiply parentheses ..

(+2x^2+18x+3x+27)-360=0

We get rid of parentheses

2x^2+18x+3x+27-360=0

We add all the numbers together, and all the variables

2x^2+21x-333=0

a = 2; b = 21; c = -333;
Δ = b2-4ac
Δ = 212-4·2·(-333)
Δ = 3105
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:

$\sqrt{\Delta}=\sqrt{3105}=\sqrt{9*345}=\sqrt{9}*\sqrt{345}=3\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{345}}{2*2}=\frac{-21-3\sqrt{345}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{345}}{2*2}=\frac{-21+3\sqrt{345}}{4}
$