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

## This Post Has 3 Comments

1. Arrrra says:

\begin{aligned}5(9x^2+9x+10) &= x(9x-40)\\&=9x^2-40x\end{aligned}\\\\ 45x^2+45x+50=9x^2-40x\\\\ (45-9)x^2+(45+40)x+50=0\\\\ 36x^2+85x+50=0

We can estimate the discriminant, and then, the solutions and we take the largest one.

$\Delta=b^2-4ac=85^2-4*36*50=25=5^2\\\\x_1=\dfrac{-85-5}{2*36}=\dfrac{-18*5}{18*4}=\dfrac{-5}{4}\\\\x_2=\dfrac{-85+5}{2*36}=\dfrac{-80}{72}=\dfrac{-8*10}{8*9}=\boxed{\dfrac{-10}{9}}$

Thank you

2. msab3253 says:

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.

3. Drew2844 says:

The expression $\frac{x+1}{8x^{2}-65x+8}$ is undefined when its denominator is zero. The denominator factors as
(x-8)(8x -1)
so it will be zero for x = 1/8 and x = 8.

The largest value of x for which the expression is undefined is 8.