To finish our problem, we need
to solve the quadratic equation
6x squared plus
x minus 51 equals
0, which we can do using the
quadratic formula, which tells
us the roots of ax squared plus
bx plus c equals zero are given
by the formula negative b plus
or minus the square root of b
squared minus 4ac all over 2a.
Where, in our example here, a,
the coefficient of x squared,
is 6, b, the
coefficient of x, is 1
and c, our constant
coefficient, is negative 51,
which when we put into
the quadratic formula,
we can reduce to negative 1 plus
or minus the square root of 1
plus 1,224 all over 12.
And 1 plus 1,224 is 1,225
whose square root is 35.
So we have negative 1
plus or minus 35 over 12.
Negative 1 plus 35 is 34,
which we have over 12.
And negative 1 minus
35 is negative 36,
which we also have over 12.
These can both be reduced
to 17 over 6 and negative 3.
So we get that the
solutions to 6x
squared plus x minus
51 equals 0 are
x equals 17/6 or negative 3.
