4+4x+9=2x^2

Solution for 4+4x+9=2x^2 equation:

4+4x+9=2x^2

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

-2x^2+4x+13=0

a = -2; b = 4; c = +13;
Δ = b2-4ac
Δ = 42-4·(-2)·13
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{30}}{2*-2}=\frac{-4-2\sqrt{30}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{30}}{2*-2}=\frac{-4+2\sqrt{30}}{-4}
$