# How do you solve  10 x ^2 − 17 x = 63 ?

Feb 4, 2016

$10 {x}^{2} - 17 x = 63$

$\rightarrow 10 {x}^{2} - 17 x - 63 = 0$

Now this is a Quadratic equation (In form $a {x}^{2} + b {x}^{2} + c = 0$)

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

In this case $a = 10 , b = - 17 , c = - 63$

$\rightarrow x = \frac{- \left(- 17\right) \pm \sqrt{{\left(- 17\right)}^{2} - 4 \left(10\right) \left(- 63\right)}}{2 \left(10\right)}$

$\rightarrow x = \frac{17 \pm \sqrt{289 - \left(- 2520\right)}}{20}$

$\rightarrow x = \frac{17 \pm \sqrt{289 + 2520}}{20}$

$\rightarrow x = \frac{17 \pm \sqrt{2809}}{20}$

$\rightarrow x = \frac{17 \pm 53}{20}$

Now we can assume the two values of $x$:

$\rightarrow x = \frac{17 + 53}{20} , \frac{17 - 53}{20}$

$\rightarrow x = \frac{70}{20} , - \frac{36}{20}$

$\rightarrow x = 3 \frac{1}{2} , - 1 \frac{4}{5}$