How does 6a to the power of 2 plus 7a minus 3 factor out?

Answer 1

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First we calculate the discriminant, delta, using the formula:

delta = b2 - 4*a*c

In our case, delta = 72 - 4*6*(-3) = 121

Delta is greater than 0 which means that we have two distinct real solutions x1 & x2.

x1 is calculated using the formula:

x1 = (-b + sqrt(delta))/2a

Similarly , where 'sqrt(delta)' is the square root of delta.

x2 = (-b - sqrt(delta))/2a

In our case sqrt(delta) = sqrt(121) = 11

So, for our equation, 6*x2 + 7*x + (-3) = 0, the solutions are:

x1 = (-7 + 11)/(2*6) = 0.333333333333

x2 = (-7 - 11)/(2*6) = -1.5

EquationDeltaX1X26*x2 + 7*x + (-3) = 01210.333333333333-1.5