Rozwiąż równanie i nierówność: a) [latex] -2x^{2} +5x-3=0[/latex] b) (x-3)(x-2)=7x-30 c) [latex]-2 x^{2} +6x- frac{9}{2} extless 0[/latex] d) [latex]-4 x^{2} +12x-9 geq 0[/latex]

a) -2x² + 5x - 3 = 0 Δ =25 - 4*(-2)*(-3) = 25 - 24 = 1   √Δ=1 x = (-5-1) / (-4)    ∨   x = (-5+1) / (-4) x = -1,5   ∨   x=1 b) (x-3)(x-2) = 7x-30 x² - 2x - 3x + 6 - 7x + 30 = 0 x² - 12x + 36 = 0 Δ = 144 - 144 = 0 x = 12 / 2 x = 6 c)  -2x² + 6x - 9/2 < 0 Δ = 36 - 36 = 0 x = -6/(-4) x = 1,5 x ∈ (-∞ ; 1,5) ∪ (1,5 ; +∞) d) -4x + 12x -9 ≥ 0 Δ = 144 - 144 = 0 x = -12/(-8) x=1,5 x⊂∅