14-4x=9x^2

Solution for 14-4x=9x^2 equation:

14-4x=9x^2

We move all terms to the left:

14-4x-(9x^2)=0

determiningTheFunctionDomain
-9x^2-4x+14=0

a = -9; b = -4; c = +14;
Δ = b2-4ac
Δ = -42-4·(-9)·14
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{130}}{2*-9}=\frac{4-2\sqrt{130}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{130}}{2*-9}=\frac{4+2\sqrt{130}}{-18}
$