Question

-(3x-2) (x-6)=x(6-x)+8


Qual o resultado?

Answer 1

$-(3x-2) (x-6)=x(6-x)+8 \\ ( - 3x + 2)(x - 6) = x(6 - x) + 8$

$- 3 {x}^{2} + 18x + 2x - 12 = 6x - {x}^{2} \\ + 8 \\ - 3 {x}^{2} + {x}^{2} + 18x + 2x - 6x \\ - 12 - 8 = 0$

$- 2 {x}^{2} + 14x - 20 = 0 \div ( - 2) \\ {x}^{2} - 7x + 10= 0$

${x}^{2} - 7x + 10= 0 \\ \Delta = {b}^{2} - 4ac \\ \Delta = {( - 7)}^{2} - 4.1.10 \\ \Delta = 49 - 40\\ \Delta = 9$

$x = \frac{-b±\sqrt{ \: \Delta}}{2a} \\ x = \frac{ - ( - 7)± \sqrt{9} }{2.1} \\ x = \frac{7±3}{2}$

$x' = \frac{7 + 3}{2} = \frac{10}{2} = 5 \\ x'' = \frac{7 - 3}{2} = \frac{4}{2} = 2$

S={5,2}