2x+3x+3x^2=22

Solution for 2x+3x+3x^2=22 equation:

2x+3x+3x^2=22

We move all terms to the left:

2x+3x+3x^2-(22)=0

We add all the numbers together, and all the variables

3x^2+5x-22=0

a = 3; b = 5; c = -22;
Δ = b2-4ac
Δ = 52-4·3·(-22)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-17}{2*3}=\frac{-22}{6}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+17}{2*3}=\frac{12}{6}
=2
$