Answer
$\displaystyle \frac{2+\sqrt{10}}{2}\approx 2.581$
$\displaystyle \frac{2-\sqrt{10}}{2}\approx-0.581$
Work Step by Step
Set the $RHS$ to 0 by subtracting 3 from both sides
$2m^{2}-4m=3\qquad.../-3$
$2m^{2}-4m-3=0$
To factor the trinomial we search for
integer factors of $2\times(-3)=-6$ whose sum is $-4$ ...
... none
We can always use the quadratic formula:
(For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ )
$m=\displaystyle \frac{-(-4)\pm\sqrt{(-4)^{2}-4(2)(-3)}}{2(2)}$
$=\displaystyle \frac{4\pm\sqrt{40}}{4}=\frac{4\pm\sqrt{4\times 10}}{4}$
$=\displaystyle \frac{4\pm 2\sqrt{10}}{4}=\frac{2(2\pm\sqrt{10})}{2(2)}$
$m=\displaystyle \frac{2\pm\sqrt{10}}{2}$
Solutions:
$\displaystyle \frac{2+\sqrt{10}}{2}\approx 2.581$ and
$\displaystyle \frac{2-\sqrt{10}}{2}\approx-0.581$.
