84=(2x-18)(2x-18+8)

Solution for 84=(2x-18)(2x-18+8) equation:

84=(2x-18)(2x-18+8)

We move all terms to the left:

84-((2x-18)(2x-18+8))=0

We add all the numbers together, and all the variables

-((2x-18)(2x-10))+84=0

We multiply parentheses ..

-((+4x^2-20x-36x+180))+84=0


We calculate terms in parentheses: -((+4x^2-20x-36x+180)), so:

(+4x^2-20x-36x+180)

We get rid of parentheses

4x^2-20x-36x+180

We add all the numbers together, and all the variables

4x^2-56x+180

Back to the equation:

-(4x^2-56x+180)


We get rid of parentheses

-4x^2+56x-180+84=0

We add all the numbers together, and all the variables

-4x^2+56x-96=0

a = -4; b = 56; c = -96;
Δ = b2-4ac
Δ = 562-4·(-4)·(-96)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-40}{2*-4}=\frac{-96}{-8}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+40}{2*-4}=\frac{-16}{-8}
=+2
$