-2x2+4x+9=-3

Solution for -2x2+4x+9=-3 equation:

-2x^2+4x+9=-3

We move all terms to the left:

-2x^2+4x+9-(-3)=0

We add all the numbers together, and all the variables

-2x^2+4x+12=0

a = -2; b = 4; c = +12;
Δ = b2-4ac
Δ = 42-4·(-2)·12
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*-2}=\frac{-4-4\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*-2}=\frac{-4+4\sqrt{7}}{-4}
$