2x(9+x)=72

Solution for 2x(9+x)=72 equation:

2x(9+x)=72

We move all terms to the left:

2x(9+x)-(72)=0

We add all the numbers together, and all the variables

2x(x+9)-72=0

We multiply parentheses

2x^2+18x-72=0

a = 2; b = 18; c = -72;
Δ = b2-4ac
Δ = 182-4·2·(-72)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*2}=\frac{12}{4}
=3
$