Question

2x.(x+5)-x.(4x+1)=10

Answer 1

2x.(x +5)    -x.(4x +1) = 10
2x.x +2x.5  -x.4x -x.1 = 10
 \  /     \   /     \   /   \   /
 2x²   +10x   -4x²   -x = 10
 2x² -4x² +10x -x -10 = 0
       -2x² +9x -10 = 0                eq. do 2o. grau

Answer 2

2x.(x+5)-x.(4x+1)=102x² + 10x - 4x² - x = 10
2x² - 4x² + 9x = 10
- 2x² + 9x - 10 = 0 

a = - 2
b = 9
c = -10

Δ = b² -4 .a . c
Δ = 9² -4 . (-2) . (-10)
Δ = 81 + 8 . (-10)
Δ = 81 - 80
Δ = 1

$\mathtt{\dfrac{-b+-~\sqrt{\Delta}}{2~.~a}~~=~~\dfrac{-9+-~\sqrt{1}}{2~.~(-2)}~~=~~\dfrac{-9+-~1}{-4}} \\ \\ \\ \mathtt{x' =\dfrac{-9+1}{-4}~~=~~~\dfrac{-8}{-4}~~=~~\dfrac{8}{4}~~=~~2} \\ \\ \\ \mathtt{x'' = \dfrac{-9-1}{-4}~~=~~\dfrac{-10}{-4}~~=~~\dfrac{10}{4}~~(\div2)~~=~~\dfrac{5}{2}} \\ \\ \\ \\ \boxed{\boxed{\mathtt{Resposta: S: \dfrac{5}{2}~~e~~ 2}}}$