9=2x+6x2

Solution for 9=2x+6x2 equation:

9=2x+6x^2

We move all terms to the left:

9-(2x+6x^2)=0

We get rid of parentheses

-6x^2-2x+9=0

a = -6; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-6)·9
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{55}}{2*-6}=\frac{2-2\sqrt{55}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{55}}{2*-6}=\frac{2+2\sqrt{55}}{-12}
$