84=2x^2+6x+4

Solution for 84=2x^2+6x+4 equation:

84=2x^2+6x+4

We move all terms to the left:

84-(2x^2+6x+4)=0

We get rid of parentheses

-2x^2-6x-4+84=0

We add all the numbers together, and all the variables

-2x^2-6x+80=0

a = -2; b = -6; c = +80;
Δ = b2-4ac
Δ = -62-4·(-2)·80
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{-(-6)-26}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+26}{2*-2}=\frac{32}{-4}
=-8
$