3x+1+2x^2=45

Solution for 3x+1+2x^2=45 equation:

3x+1+2x^2=45

We move all terms to the left:

3x+1+2x^2-(45)=0

We add all the numbers together, and all the variables

2x^2+3x-44=0

a = 2; b = 3; c = -44;
Δ = b2-4ac
Δ = 32-4·2·(-44)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-19}{2*2}=\frac{-22}{4}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*2}=\frac{16}{4}
=4
$