-2x^2+4x+6=4

Solution for -2x^2+4x+6=4 equation:

-2x^2+4x+6=4

We move all terms to the left:

-2x^2+4x+6-(4)=0

We add all the numbers together, and all the variables

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

a = -2; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-2)·2
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-2}=\frac{-4-4\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-2}=\frac{-4+4\sqrt{2}}{-4}
$