2x^2+3(2x)+4=2

Solution for 2x^2+3(2x)+4=2 equation:

2x^2+3(2x)+4=2

We move all terms to the left:

2x^2+3(2x)+4-(2)=0

We add all the numbers together, and all the variables

2x^2+32x+2=0

a = 2; b = 32; c = +2;
Δ = b2-4ac
Δ = 322-4·2·2
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-12\sqrt{7}}{2*2}=\frac{-32-12\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+12\sqrt{7}}{2*2}=\frac{-32+12\sqrt{7}}{4}
$