# How to use the discriminant to find out how many real number roots an equation has for 14a^2 - a= 5a^2 - 5a?

May 18, 2015

Write it collecting all terms to the left as in:
$14 {a}^{2} - a - 5 {a}^{2} + 5 a = 0$
$9 {a}^{2} + 4 a = 0$

This is in the form:
$m {a}^{2} + n a + p = 0$
where:
$m = 9$
$n = 4$
$p = 0$
The discriminant is:
$\Delta = {n}^{2} - 4 m p = 16 - 4 \left(9 \cdot 0\right) = 16 > 0$
Your equation will give you 2 real distict solutions.
[In this case ${x}_{1} = 0 \mathmr{and} {x}_{2} = - \frac{4}{9}$]