3=2x2-4x

Solution for 3=2x2-4x equation:

3=2x^2-4x

We move all terms to the left:

3-(2x^2-4x)=0

We get rid of parentheses

-2x^2+4x+3=0

a = -2; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-2)·3
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*-2}=\frac{-4-2\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*-2}=\frac{-4+2\sqrt{10}}{-4}
$