X+4-2x^2=2

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

X+4-2X^2=2

We move all terms to the left:

X+4-2X^2-(2)=0

We add all the numbers together, and all the variables

-2X^2+X+2=0

a = -2; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-2)·2
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{17}}{2*-2}=\frac{-1-\sqrt{17}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*-2}=\frac{-1+\sqrt{17}}{-4}
$