# Use the quadratic formula to solve the equation:6x^2 + 5x -3 = 0

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Given the quadratic equation:

6x^2 + 5x -3 = 0

Then we know that a = 6 b= 5 and c = -3

We will use the quadratic formula to find the roots.

We know that:

x = [ -b +- sqrt(b^2-4ac)] / 2a

==> x1 = [ -5 + sqrt(25+4*6*3)]/ 2*6

= ( -5 + sqrt97) / 12

==> x2= ( -5-sqrt97)/12

Then the roots are:

**x = { (-5+sqrt97)/12 , (-5-sqrt97)/12 } **

The solutions of the quadratic equation ax^2 + bx + c = 0 are given by [ -b + sqrt (b^2 - 4ac)]/2a and [ -b - sqrt (b^2 - 4ac)]/2a

The equation we have here is 6x^2 + 5x - 3 = 0

a = 6, b = 5 , c = -3

Substituting the values in the formula we get

x1 = [ -5 + sqrt (25 + 72)]/12

=> -5/12 + sqrt 97/12

x2 = -5/12 - sqrt 97/12

**The solution of the equation are (-5/12 + sqrt 97/12, -5/12 - sqrt 97/12)**