Question

2x-5=7
5-x=9-3x
x²-7x+12=0
2x²-5x+3=0
-x²+7x=0
X²+3x+10=0

Answer 1

x²-7x+12=0

(x-4)(x-3)=0

x-4=0

x-3=0

x={4,3}

-x²+7x=0

x(7-x)=0

x=0

7-x=0

x={0,7}

Answer 2

2 x - 5 = 7

2 x = 7 + 5

2 x = 12

x = 12 : 2

x = 6

____________

5 - x = 9 - 3 x

- x + 3 x = 9 - 5

2 x = 4

x = 4 : 2

x = 2

____________

x² - 7 x + 12 = 0

Δ= 49 - 4 × 12 = 1

x₁ = ( 7 + √1 ) / 2 = 8 / 2 = 4

x₂ = ( 7 - 1 ) / 2 = 6 / 2 = 3

_________________________

2 x² - 5 x + 3 = 0

Δ = 25 - 4 × 2 × 3 = 25 - 24 = 1

x₁ = ( 5 + √1 ) / ( 2 × 2 ) = 6 / 4 = 3 / 2 = 1,5

x₂ = ( 5 - 1 ) / 4 = 4 / 4 = 1

___________________________

- x² + 7 x = 0

x ( 7 - x ) = 0

x₁ = 0

7 - x = 0 ⇒ x₂ = 7

_______________

x² + 3 x + 10 = 0

Δ = 9 - 40 = - 31 ; Δ < 0 ⇒ x₁, ₂ ∉ R

x² + 3 x - 10 = 0

Δ = 9 + 40 = 49

x₁ = ( - 3 + √49 ) / 2 = ( - 3 + 7 ) / 2 = 4 / 2 = 2

x ₂ = ( - 3 - 7 ) / 2 = ( - 10 ) / 2 = - 5