Solve the equation?

Question

and express the roots in a + bi form


Second question

Solve for X Fraction 5/3x - Fraction 6/4x = Fraction 1/6

9x^2 - 30x + 34 = 0

Where does this 900 come from. I am still confused sorry :(

Answer 1

5/3 x - 6/4 x = 1/6

Multuply through by 12 (least common multiple) to get rid of fractions:

12(5/3)x - 12(6/4)x = 12(1/6)

20x - 18x = 2
2x = 2
x = 1

Double check:

5/3(1) - 6/4(1) = 1/6
20/12 - 18/12 = 2/12 check.

Your second problem:

9x² - 30x + 34 = 0

Doesn't factor, because the discriminant is negative:

x = (30 ± √(900 - 4(9)34))/(2(9))
x = (30 ± √(-324))/18
x = (30 ± 18i)/18
x = 5/3 ± i

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The 900 comes from the "discriminant", the part under the √ sign. It's b² - 4ac = (30)² - 4(9)34 = 900 - 1224...

Answer 2

x= (30 +- sqrt(900-1224)/18 = 30/18 +- i = 5/3+-i

(20x-18x)/12x^2= 1/6 ===> 2x=2 x^2
x can not be zero(it is dividing) so x=1