(6x+4)(4x+8)=84

Solution for (6x+4)(4x+8)=84 equation:

(6x+4)(4x+8)=84

We move all terms to the left:

(6x+4)(4x+8)-(84)=0

We multiply parentheses ..

(+24x^2+48x+16x+32)-84=0

We get rid of parentheses

24x^2+48x+16x+32-84=0

We add all the numbers together, and all the variables

24x^2+64x-52=0

a = 24; b = 64; c = -52;
Δ = b2-4ac
Δ = 642-4·24·(-52)
Δ = 9088
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:

$\sqrt{\Delta}=\sqrt{9088}=\sqrt{64*142}=\sqrt{64}*\sqrt{142}=8\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{142}}{2*24}=\frac{-64-8\sqrt{142}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{142}}{2*24}=\frac{-64+8\sqrt{142}}{48}
$