# Given f(x)=x²+3x-5 and g(x)=2x-3, how do you determine x when f(x)=g(x)?

Feb 4, 2017

The solutions are $S = \left\{- 1 , 2\right\}$

#### Explanation:

$f \left(x\right) = {x}^{2} + 3 x - 5$

$g \left(x\right) = 2 x - 3$

$f \left(x\right) = g \left(x\right)$

${x}^{2} + 3 x - 5 = 2 x - 3$

${x}^{2} - x - 2 = 0$

We can solve this quadratic equation by factorization

$\left(x + 1\right) \left(x - 2\right) = 0$

$x - 1 = 0$, $\implies$, $x = - 1$

$x - 2 = 0$, $\implies$, $x = 2$