9x+5x^2-2+3x-2x^2=14

Solution for 9x+5x^2-2+3x-2x^2=14 equation:

9x+5x^2-2+3x-2x^2=14

We move all terms to the left:

9x+5x^2-2+3x-2x^2-(14)=0

We add all the numbers together, and all the variables

3x^2+12x-16=0

a = 3; b = 12; c = -16;
Δ = b2-4ac
Δ = 122-4·3·(-16)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*3}=\frac{-12-4\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*3}=\frac{-12+4\sqrt{21}}{6}
$