(2x+9)(6+x)=0

Solution for (2x+9)(6+x)=0 equation:

(2x+9)(6+x)=0

We add all the numbers together, and all the variables

(2x+9)(x+6)=0

We multiply parentheses ..

(+2x^2+12x+9x+54)=0

We get rid of parentheses

2x^2+12x+9x+54=0

We add all the numbers together, and all the variables

2x^2+21x+54=0

a = 2; b = 21; c = +54;
Δ = b2-4ac
Δ = 212-4·2·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3}{2*2}=\frac{-18}{4}
=-4+1/2
$