# How do you solve -2x^2+13x=15?

Jul 31, 2017

$- 2 {x}^{2} + 13 x = 15$

$\implies$

$x = 5 \mathmr{and} x = \frac{3}{2}$

#### Explanation:

Remember the standard form of a quadratic is $a {x}^{2} + b x + c$

So first we put the equation into standard form

$- 2 {x}^{2} + 13 x = 15$

$\iff$ subtract $15$ from both sides

$- 2 {x}^{2} + 13 x - 15 = 0$

Then we can factor this equation

$\left(- 2 x + 3\right) \left(x - 5\right) = 0$

Then we see that $x$ could equal $5$

or

$\left(- 2 x + 3\right) = 0$

$\iff$

$- 2 x = - 3$

$\iff$

$x = \frac{3}{2}$

$\therefore x = 5 \mathmr{and} x = \frac{3}{2}$