Answer
{$\frac{2 \pm \sqrt (10)}{2}$}
Work Step by Step
Step 1: Comparing $-2x^{2}+4x+3=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$;
$a=-2$, $b=4$ and $c=3$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt (b^{2}-4ac)}{2a}$
Step 3: Substituting the values of a,b and c in the formula:
$x=\frac{-(4) \pm \sqrt ((4)^{2}-4(-2)(3))}{2(-2)}$
Step 4: $x=\frac{-4 \pm \sqrt (16+24)}{-4}$
Step 5: $x=\frac{-4 \pm \sqrt (40)}{-4}$
Step 6: $x=\frac{-4 \pm \sqrt (4\times10)}{-4}$
Step 7: $x=\frac{-4 \pm 2\sqrt (10)}{-4}$
Step 8: $x=\frac{2(-2 \pm \sqrt (10))}{-4}$
Step 9: $x=\frac{-2 \pm \sqrt (10)}{-2}$
Step 10: $x=\frac{-2+\sqrt (10)}{-2}$ or $x=\frac{-2-\sqrt (10)}{-2}$
Step 11: $x=\frac{-1(2-\sqrt (10))}{-2}$ or $x=\frac{-1(2+\sqrt (10))}{-2}$
Step 12: $x=\frac{2-\sqrt (10)}{2}$ or $x=\frac{2+\sqrt (10)}{2}$
Step 13: Therefore, the solution set is {$\frac{2 \pm \sqrt (10)}{2}$}.
