84=(x+3)(2x+8)

Solution for 84=(x+3)(2x+8) equation:

84=(x+3)(2x+8)

We move all terms to the left:

84-((x+3)(2x+8))=0

We multiply parentheses ..

-((+2x^2+8x+6x+24))+84=0


We calculate terms in parentheses: -((+2x^2+8x+6x+24)), so:

(+2x^2+8x+6x+24)

We get rid of parentheses

2x^2+8x+6x+24

We add all the numbers together, and all the variables

2x^2+14x+24

Back to the equation:

-(2x^2+14x+24)


We get rid of parentheses

-2x^2-14x-24+84=0

We add all the numbers together, and all the variables

-2x^2-14x+60=0

a = -2; b = -14; c = +60;
Δ = b2-4ac
Δ = -142-4·(-2)·60
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*-2}=\frac{40}{-4}
=-10
$