Question

x^2/ 6= x/3-1/2=

x^2-9x=0

x^2-25=0

Answer 1

a)
X² - 9X = 0
X² = 9X
X²/X = 9
X = 9.

b)
X² - 25 = 0
X² = 25
X = √25
X = 5.

Answer 2

$\frac{x^2}{6}= \frac{x}{3}- \frac{1}{2} \\ \\ \frac{x^2}{6}= \frac{2x}{6}- \frac{3}{6} \\ \\x^2=2x-3 \\ \\ x^2-2x+3=0\to x_{1y2}= \frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ x_{1y2}= \frac{-2\pm \sqrt{4-4(1)(3)}}{2(1)} \\ \\ x_{1y2}= \frac{-2\pm \sqrt{4-12}}{2} \\ \\ x_{1y2}= \frac{-2\pm \sqrt{-8}}{2} \to No \ hay \ soluci\'on\ real$

$x^2-9x=0\qquadsacamos \ factor \ com\'un \\ \\ x(x-9)=0 \\ \\x=0\qquad \qquad x-9=0\to x=9, \\ \\ entonces \ hay \ dos \ resultados\to \ x_1=0\qquad x_2=9 \\ \\ \\ x^2-25= 0 \\ \\ x^2= 25 \\ \\ x=\pm \sqrt{25} \\ \\ x_1=5\qquad \qquad x_2=-5$

Espero que te sirva, salu2!!!!