An algebra problem by A Former Brilliant Member

Let the roots of the quadratic equation $ax^2+bx+c=0$ be $x_1$ and $x_2$ .

By using the Vieta’s Formula , the product of roots is

$(x_1)(x_2)=\dfrac{c}{a}$

Substituting, we get

$4=\dfrac{2h-5}{3}$

$12=2h-5$

$17=2h$

$\dfrac{17}{2}=h$

$8.5=h$