Решить уравнение: 3 (6x^2-13x+6) ^2-10 (6x^2-13x) = 53

K=6x^2-13x+6

6x^2-13x=k-6

3 (6x^2-13x+6) ^2-10 (6x^2-13) = 53

3k^2-10 (k-6) = 53

3k^2-10k+60-53=0

3k^2-10k+7=0

k1 = (- (-10) - (10^2-4*3*7) ^-2) / (2*6) = (10 - (100-84) ^-2) / 12=0,5

k2 = (- (-10) + (10^2-4*3*7) ^-2) / (2*6) = (10 + (100-84) ^-2) / 12=7/6=1.167

6x^2-13x+6=0,5 6x^2 - 13x+5,5=0

x1 = (13 - (13^2-4*6*5,5) ^-2) / 2*6 = (13-37^-2) / 12=0,576

x1 = (13 + (13^2-4*6*5,5) ^-2) / 2*6 = (13+37^-2) / 12=1,59

6x^2-13x+6=7/6 6x^2 - 13x+4 (5/6) = 0

x1 = (13 - (13^2-4*6 * (29/6)) ^-2) / 2*6 = (13-57^-2) / 12=0,477

x1 = (13 + (13^2-4*6 * (29/6)) ^-2) / 2*6 = (13+57^-2) / 12=1,69

Ответ: x1=0,576; x2=1.59; x3=0.477; x4=1.69.