Question

(6x−18)2−5(6x−18)+6=0

Answer 1

(6х-18)²-5(6х-18)+6=0

36х²-216х+324-30х+90+6=0

36х²-246х+420=0|:3

12х²-82х+140=0|:2

6х²-41х+70=0

х1,2=41±√-41²-4*6*70/2*6=
=41±1/12

х1=41+1/12=42/12=3,5
х2=41-1/12=40/12=3 1/3

Answer 2

To solve the quadratic equation (6x−18)²−5(6x−18)+6=0, let's first simplify it and then find the solutions for x.

Let's substitute y = (6x−18) to make the equation easier to work with:

y² - 5y + 6 = 0

Now, we can factor this quadratic equation:

(y - 2)(y - 3) = 0

Now, set each factor to zero and solve for y:

1. y - 2 = 0 y = 2

2. y - 3 = 0 y = 3

Now, remember that y = (6x - 18), so we can set each of these equal to (6x - 18) and solve for x:

1. 6x - 18 = 2 6x = 20 x = 20/6 x = 10/3

2. 6x - 18 = 3 6x = 21 x = 21/6 x = 7/2

So, the solutions for the given equation are x = 10/3 and x = 7/2.