14-2x=9x^2

Solution for 14-2x=9x^2 equation:

14-2x=9x^2

We move all terms to the left:

14-2x-(9x^2)=0

determiningTheFunctionDomain
-9x^2-2x+14=0

a = -9; b = -2; c = +14;
Δ = b2-4ac
Δ = -22-4·(-9)·14
Δ = 508
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:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{127}}{2*-9}=\frac{2-2\sqrt{127}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{127}}{2*-9}=\frac{2+2\sqrt{127}}{-18}
$