Question

Реши квадратное уравнение 4(5x−9)2−11(5x−9)+6=0..

Answer 1

$4(5x-9)^2-11(5x-9)+6=0\\4(25x^2-90x+81)-55x+99+6=0\\100x^2-360x+324-55x+99+6=0\\100x^2-415x+429=0\\D=415^2-4*429*100=172225-171600=625\\D>0=> x_1, x_2\\x_1=\frac{-(-415)+\sqrt{625} }{2*100} =\frac{440}{200} =\frac{11}{5}=2,2 \\x_1=\frac{-(-415)-\sqrt{625} }{2*100} =\frac{390}{200} =\frac{39}{20} =1,95$