(2c+9)(c-6)=0

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

(2c+9)(c-6)=0

We multiply parentheses ..

(+2c^2-12c+9c-54)=0

We get rid of parentheses

2c^2-12c+9c-54=0

We add all the numbers together, and all the variables

2c^2-3c-54=0

a = 2; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·2·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*2}=\frac{-18}{4}
=-4+1/2
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*2}=\frac{24}{4}
=6
$