Уравнение 2х(3х-1)=5(х+1)

[latex]2x(3x-1)=5(x+1)[/latex] [latex]6 x^{2} - 2x=5x+5[/latex] [latex]6 x^{2} -2x-5x-5=0[/latex] [latex]6 x^{2} -7x-5=0[/latex] [latex]6 x^{2} -7x-5=0[/latex] [latex]D= b^{2} - 4ac = (-7)^{2} - 4*6*(-5) = [latex]49+120=169[/latex] [latex] \sqrt{D} = \sqrt{169} =13[/latex] [latex] x_{1}= \frac{7+13}{2*6} = \frac{20}{12} =1 \frac{2}{3} [/latex] [latex] x_{2} = \frac{7-13}{2*6} = \frac{-6}{12} =-0,5[/latex] Ответ:x∈(-бесконечность;-0,5)U([latex]1 \frac{2}{3} [/latex];+бесконечность)