Question

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 5.$$Find the largest value of x such that 3x^2 + 17x + 15 = 5.$

Answer 1

The largest x that satisfies

$3x^2+17x+15=5$

is the largest solution to

$3x^2+17x+10=0$

We have

$3x^2+17x+10=(3x+2)(x+5)=0$

$\implies x=-\dfrac23\text{ or }x=-5$

and so the largest value of x we want is -2/3.