12a 2 −22a−5=−5a

Sure, let's solve the equation step by step:

12a^2 - 22a - 5 = -5a

Step 1: Bring all terms to one side of the equation:

12a^2 - 22a + 5a - 5 = 0

Step 2: Simplify the equation:

12a^2 - 17a - 5 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it using the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / 2a.

Step 3: Identify a, b, and c in the equation:

a = 12, b = -17, c = -5

Step 4: Substitute a, b, and c into the quadratic formula:

a1,2 = [17 ± sqrt((-17)^2 - 412(-5))] / 2*12

Step 5: Simplify under the square root:

a1,2 = [17 ± sqrt(289 + 240)] / 24

Step 6: Further simplify:

a1,2 = [17 ± sqrt(529)] / 24

Step 7: Take the square root:

a1,2 = [17 ± 23] / 24

So, the solutions are:

a1 = 40 / 24 = 5/3

a2 = -6 / 24 = -1/4