How do you solve 2x^2 - 3x + 4 = 0?

May 16, 2015

This is a quadratic equation of the form:
$a {x}^{2} + b x + c = 0$
Where:
$a = 2$
$b = - 3$
$c = 4$
So you can use the Quadratic Formula:
${x}_{1 , 2} = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$= \frac{3 \pm \sqrt{9 - 32}}{4}$
The negative argument of the square root tells you that you will not get Real solutions (you'll get Complex Solutions).
${x}_{1 , 2} = \frac{3 \pm \sqrt{- 1 \cdot 23}}{4} = \frac{3 \pm i \sqrt{23}}{4}$
Where $i = \sqrt{- 1}$