x+2x^2+3x+2=180

Solution for x+2x^2+3x+2=180 equation:

x+2x^2+3x+2=180

We move all terms to the left:

x+2x^2+3x+2-(180)=0

We add all the numbers together, and all the variables

2x^2+4x-178=0

a = 2; b = 4; c = -178;
Δ = b2-4ac
Δ = 42-4·2·(-178)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12\sqrt{10}}{2*2}=\frac{-4-12\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12\sqrt{10}}{2*2}=\frac{-4+12\sqrt{10}}{4}
$