Using the quadratic formula solver Example 3

Solve $2x^2-6x+3=0$

$x=(-b+-sqrt(b^2-4ac))/(2a)$

Therefore $a=2$ , $b=-6$ & $c=3$

$x=(-(-6)+-sqrt((-6)^2-4times2times3))/(2times2)$

$x=(6+-sqrt(36-24))/4$

$x=(6+-sqrt12)/4$

$x=(6+sqrt12)/4$ or $x=(6-sqrt12)/4$

Using a calculator we get

$x=(6+3.464)/4$ or $x=(6-3.464)/4$

$x=2.366$ or $x=0.634$

$2x^2-6x+3=0$

If $x=2.366$ $2times2.366^2-6times2.366+3=0$

$11.19-14.19+3=0$ Which is correct

If $x=0.634$ $2times0.634^2-6times0.634+3=0$

$0.804-3.804+3=0$ Which is correct

Answer:

The roots of $2x^2-6x+3=0$ are $x=2.366$ or $x=0.634$

Quick stetch example 3