How do you solve  25x²=20x+6 using the quadratic formula?

Apr 29, 2016

$x = \frac{2 + \sqrt{10}}{5} \mathmr{and} x = \frac{2 - \sqrt{10}}{5}$

Explanation:

$25 {x}^{2} = 20 x + 6$
$\implies 25 {x}^{2} - 20 x - 6 = 0$
$\implies {\left(5 x\right)}^{2} - 2.5 x .2 + {2}^{2} - 4 - 6 = 0$
$\implies {\left(5 x\right)}^{2} - 2.5 x .2 + {2}^{2} = 4 + 6$
$\implies {\left(5 x - 2\right)}^{2} = 10$
$\implies \left(5 x - 2\right) = \pm \sqrt{10}$
$\therefore x = \frac{2 + \sqrt{10}}{5} \mathmr{and} x = \frac{2 - \sqrt{10}}{5}$