Respuesta:
Ecuación
[tex]7x(x-2)=3x(x+2) \\ 7 {x}^{2} - 14x = 3 {x}^{2} + 6x \\ \boxed{7 {x}^{2}} - 14x - \boxed{3 {x}^{2}} - 6x = 0 \\ 4 {x}^{2} - \boxed{14x} - \boxed{6x} = 0 \\ 4 {x}^{2} - 20x = 0 [/tex]
Factor común: 4
[tex]4 {x}^{2} - 20x = 0 \\ 4( {x}^{2} - 5x) = 0[/tex]
[tex] {x}^{2} - 5x = 0[/tex]
Fórmula cuadrática
[tex] \boxed{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac}}{2a}} [/tex]
[tex] {x}^{2} - 5x = 0 [/tex]
a = 1
b = -5
c = 0
[tex]x = \frac{ - ( - 5)± \sqrt{( - 5)^{2} - 4 \times 1 \times 0 } }{2 \times 1} [/tex]
[tex]x = \frac{ - ( - 5)± \sqrt{{( - 5)}^{2} - 0} }{2} [/tex]
[tex]x = \frac{ - ( - 5)± \sqrt{25} }{2} [/tex]
[tex]x = \frac{ - ( - 5)±5}{2} [/tex]
[tex]x = \frac{5±5}{2} [/tex]
[tex]x = \frac{5 + 5}{2} = \frac{10}{2} = \boxed{5} \\ x = \frac{5 - 5}{2} = \frac{0}{2} = \boxed{0}[/tex]
Solución
[tex] \boxed{x = 5}[/tex]
[tex] \boxed{x = 0}[/tex]
Espero te sirva :)
