x+3x-2+3x2=45

Solution for x+3x-2+3x2=45 equation:

x+3x-2+3x^2=45

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2+4x-47=0

a = 3; b = 4; c = -47;
Δ = b2-4ac
Δ = 42-4·3·(-47)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{145}}{2*3}=\frac{-4-2\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{145}}{2*3}=\frac{-4+2\sqrt{145}}{6}
$