# How do you find the roots of 2x^2+ 7x -3 =x^2 +3x using any method you choose?

Oct 23, 2016

We start by putting all terms to one side of the equation.

$2 {x}^{2} - {x}^{2} + 7 x - 3 x - 3 = 0$

Next, combine like terms.

${x}^{2} + 4 x - 3 = 0$

Since we are dealing with small numbers, we can easily discover whether or not this trinomial is factorable, and if it is, factor it. However, no two numbers add to $4$ and multiply to $- 3$. Hence, we will need to solve using what I find to be the next easiest method: the quadratic formula.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{- 4 \pm \sqrt{{4}^{2} - 4 \times 1 \times - 3}}{2 \times 1}$

$x = \frac{- 4 \pm \sqrt{28}}{2}$

$x = \frac{- 4 \pm 2 \sqrt{7}}{2}$

$x = \pm \sqrt{7} - 2$

Hopefully this helps!