solve by completing the square. 2 x 2 + 2 x − 3 = 0

$2x^2+2x-3=0$
Divide through bywhatever is multiplied on the squared term.
$x^2+x-\frac{3}{2}=0$
Take half of thecoefficient (don't forget the sign!) of the x-term, and square it. Add thissquare to both sides of the equation.
$x^2+x-\frac{3}{2}+.25=.25$
Bring the 3/2 over toother side
$x^2+x+.25=\frac{3}{2}+.25$
$(x+5{)}^2=1.75$
square root both sides
$x\pm .5=\sqrt{1.75}$
$x=\sqrt{1.75}\pm .5$
$x=\sqrt{\frac{7}{4}}\pm \frac{1}{2}$
and this can be rewrote:
$x=\frac{\sqrt{7}}{2}\pm \frac{1}{2}$
$x=\frac{1\pm \sqrt{7}}{2}$

I would use the quadratic formula which is:$(-b\pm \sqrt{b^2-4ac})/2a$
Using that:
$(-2\pm \sqrt{22-4(2)(-3)})/2(2)=(-2\pm \sqrt{28})/4$