3x+2x^2+5x+2=452

Solution for 3x+2x^2+5x+2=452 equation:

3x+2x^2+5x+2=452

We move all terms to the left:

3x+2x^2+5x+2-(452)=0

We add all the numbers together, and all the variables

2x^2+8x-450=0

a = 2; b = 8; c = -450;
Δ = b2-4ac
Δ = 82-4·2·(-450)
Δ = 3664
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:

$\sqrt{\Delta}=\sqrt{3664}=\sqrt{16*229}=\sqrt{16}*\sqrt{229}=4\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{229}}{2*2}=\frac{-8-4\sqrt{229}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{229}}{2*2}=\frac{-8+4\sqrt{229}}{4}
$