# How do you solve x^2 + 3x - 5 = 0?

Nov 1, 2015

x = $\frac{- 3 + \sqrt{29}}{2}$ or $x = \frac{- 3 - \sqrt{29}}{2}$

#### Explanation:

This equation does not easily factorise so using the general equation $y = a {x}^{2} + b x + c$ and the formula

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

then if $y = {x}^{2} + 3 x - 5$

a =1, b = 3 and c = -5

$x = \frac{- 3 + \sqrt{{3}^{2} - \left(- 20\right)}}{2}$ or$x = \frac{- 3 - \sqrt{{3}^{2} - \left(- 20\right)}}{2}$

which comes to the given answer.
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