2 x - 5 = 7
2 x = 7 + 5
2 x = 12
x = 12 : 2
x = 6
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5 - x = 9 - 3 x
- x + 3 x = 9 - 5
2 x = 4
x = 4 : 2
x = 2
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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
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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
