(2x+6)(2x+9)=54

Solution for (2x+6)(2x+9)=54 equation:

(2x+6)(2x+9)=54

We move all terms to the left:

(2x+6)(2x+9)-(54)=0

We multiply parentheses ..

(+4x^2+18x+12x+54)-54=0

We get rid of parentheses

4x^2+18x+12x+54-54=0

We add all the numbers together, and all the variables

4x^2+30x=0

a = 4; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·4·0
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{-(30)-30}{2*4}=\frac{-60}{8}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*4}=\frac{0}{8}
=0
$