(2x+6)(4x-18)=36

Solution for (2x+6)(4x-18)=36 equation:

(2x+6)(4x-18)=36

We move all terms to the left:

(2x+6)(4x-18)-(36)=0

We multiply parentheses ..

(+8x^2-36x+24x-108)-36=0

We get rid of parentheses

8x^2-36x+24x-108-36=0

We add all the numbers together, and all the variables

8x^2-12x-144=0

a = 8; b = -12; c = -144;
Δ = b2-4ac
Δ = -122-4·8·(-144)
Δ = 4752
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:

$\sqrt{\Delta}=\sqrt{4752}=\sqrt{144*33}=\sqrt{144}*\sqrt{33}=12\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{33}}{2*8}=\frac{12-12\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{33}}{2*8}=\frac{12+12\sqrt{33}}{16}
$