X² + 2x - 24 = 0
D = 2² - 4*1*(-24) = 4 + 96 = 100 = 10²
D > 0
x₁ = ( - 2 - 10)/(2*1) = -12/2 = - 6
x₂ = ( - 2 + 10)/(2*1) = 8/2 = 4
x² + 8x - 13 =0
D = 8² - 4*1*(-13) = 64 + 52= 116 = ( 2√29 )²
D> 0
x₁ = ( - 8 - 2√29)/(2*1) = - 4 -√29 = - (4 + √29)
x₂ = ( - 8 + 2√29)/(2*1)= - 4 + √29 =√29 - 4
21x²-2x - 3 = 0
D = (-2)² - 4*21*(-3) = 4 + 252 = 256 =16²
D>0
x₁ = ( - (-2) - 16)/(2*21) = (2 - 16)/42 = - 14/42 = - 1/3
x₂ = ( - (-2) + 16)/(2 *21) = (2+ 16)/42 = 18/42 = 3/7