Answer
$(-5,35)$, $(7,155)$
Work Step by Step
Given $$
\begin{cases}
& y=3 x^2+4 x-20 \\
& y=2 x^2+6 x+15
\end{cases}.
$$ Set the two equations equal and solve for the values of $x$.
$$
\begin{aligned}
3 x^2+4 x-20&=2 x^2+6 x+15 \\
(3-2) x^2+(4-6) x&=15+20 \\
x^2-2 x+y^2&=35 \\
(x-1)^2&=36\\
x-1&= \pm \sqrt{36} \\
x-1&= \pm 6 \\
x=1& \pm 6
\end{aligned}
$$ The solutions are: $$
\begin{aligned}
x_1 & =1-6 \\
& =-5 \\
x_2 & =1+6 \\
& =7.
\end{aligned}
$$ Find the corresponding $y$ values using either of the given equations.
$$
\begin{aligned}
y_1&=3\cdot (-5)^2+4\cdot(-5)-20 = 35\\
y_2&=3\cdot (7)^2+4\cdot(7)-20 = 155.
\end{aligned}
$$ Plot the two functions in the same window to check the solution(s).
The solution is $(-5,35)$ and $(7,155)$.
