Question

What are the roots of x in -10x^2+12x-9=0​

Answer 1

$- 10 {x}^{2} + 12x - 9 = 0 \\ \Leftrightarrow {x}^{2} - \frac{6}{5} x + \frac{9}{10 } = 0 \\ \Leftrightarrow {x}^{2} - \frac{6}{5}x + \frac{9}{25} = - \frac{9}{10} + \frac{9}{25} \\ \Leftrightarrow \underbrace{ {(x - \frac{3}{5} )}^{2} }_{ \geqslant 0} = - \frac{27}{50} \\ \Leftrightarrow x\in\emptyset \\ \Rightarrow Roots: None$