# How do you solve 7x ^ { 2} + 37x - 30= 0?

May 17, 2018

$x = \frac{5}{7} \mathmr{and} x = - 6$

#### Explanation:

This is a quadratic equation in the form of $a {x}^{2} + b x + c = 0$.

First, you multiply $a$ and $c$, in this case, $7$ and $- 30$, and get $- 210$. Then you get factors of $a c$ $\left(- 210\right)$ which when added give $b$ $\left(37\right)$.

The factors are $42$ and $- 5$. You substitute this factors in place of $b$

$\left(7 {x}^{2} + 42 x\right) \left(- 5 x - 30\right) = 0$

$7 x \left(x + 6\right) - 5 \left(x + 6\right) = 0$

$7 x - 5 = 0 \implies x = \frac{5}{7}$

$x + 6 = 0 \implies x = - 6$

May 17, 2018

Solution: $x = - 6 , x = \frac{5}{7}$

#### Explanation:

$7 {x}^{2} + 37 x - 30 = 0$ or

$7 {x}^{2} + 42 x - 5 x - 30 = 0$ or

$7 x \left(x + 6\right) x - 5 \left(x + 6\right) = 0$ or

$\left(x + 6\right) \left(7 x - 5\right) = 0 \therefore$ either $x + 6 = 0 \therefore x = - 6.$ or

$7 x - 5 = 0 \therefore x = \frac{5}{7}$

Solution: $x = - 6 , x = \frac{5}{7}$ [Ans]