We are given this equation:
[tex] 2x^{2} -12x+20=0 [/tex]
Let us use quadratic formula to find its solution.
The quadratic formula for general quadratic equation of the form ax²+bx+c=0 is given by:
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
Now on comparing our equation with this general form our a, b and c are:
a=2, b=-12 and c=20
Plugging these values in the formula:
[tex]x=\frac{-(-12))\pm \sqrt{(-12)^{2}-4(2)(20)}}{2(2))}[/tex]
On solving we will get,
[tex]x=\frac{(12))\pm \sqrt{(144)-(160)}}{(4)}[/tex]
Simplifying we will get,
[tex]x=\frac{(12))\pm \sqrt{-16}}{(4)}[/tex]
square root of -1 is "i".
[tex]x=\frac{(12))\pm \-4i}{(4)}[/tex]
taking 4 common out as gcf in numerator,
[tex] x=3\pm i [/tex]
Answer : x=3+i and x=3-i
