Question

f%20%24x%24%20such%20that%20%243x%5E2%20%2B%2017x%20%2B%2015%20%3D%205.%24" id="TexFormula1" title="Find the largest value of $x$ such that $3x^2 + 17x + 15 = 5.$" alt="Find the largest value of $x$ such that $3x^2 + 17x + 15 = 5.$" align="absmiddle" class="latex-formula">

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.