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Please help quick!!

What is the solution set of the following equation? 6x 2 = 13x + 5
{5/3, -1/2}
{-1/3, 5/2}
{-3, 2/5}

User Dream Lane
by
8.1k points

2 Answers

7 votes
C
6x^2-13X-5=0
(3X+1)(2X-5)
3x-1=0
X=1/3. 2x-5=0. X= 5/2
User Derigel
by
8.9k points
2 votes

Answer:

Option A is correct.


\{(5)/(3), -(1)/(3)\}

Explanation:

Given the equation:
6x^2=13x+5

we can write this as:


6x^2-13x-5=0

A quadratic equation is of the form:
ax^2+bx+c=0

then the solution is given by:


x = (-b\pm√(b^2-4ac))/(2a)

On comparing with the given equation we have;

a = 6, b = -13 and c = -5 then;

Substitute the given values we have


x = (-(-13)\pm√((-13)^2-4(6)(-5)))/(2(6))


x = (13\pm√(169+120))/(12)

Simplify:


x = (13 \pm√(289))/(12)


x = (13 \pm 17)/(12)

Then;


x = (13+17)/(12) and
x = (13-17)/(12)


x = (20)/(12) and
x = -(4)/(12)


x = (5)/(3) and
x = -(1)/(3)

Therefore, the solution for the given equation are:


\{(5)/(3), -(1)/(3)\}

User Toni Rmc
by
7.1k points

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