55=3x+2x^2

Solution for 55=3x+2x^2 equation:

55=3x+2x^2

We move all terms to the left:

55-(3x+2x^2)=0

We get rid of parentheses

-2x^2-3x+55=0

a = -2; b = -3; c = +55;
Δ = b2-4ac
Δ = -32-4·(-2)·55
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{449}}{2*-2}=\frac{3-\sqrt{449}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{449}}{2*-2}=\frac{3+\sqrt{449}}{-4}
$