Let $X∼N(\mu_1,\sigma_1^2)$ and $Y∼N(\mu_2,\sigma_2^2)$ be two independent normal variables. find $x$ so $\Phi(x)=P(X_1<4X_2)$.

Question

Let $X\sim N(\mu_1,\sigma_1^2)$ and $Y\sim N(\mu_2,\sigma_2^2)$ be two independent normal variables. calculate $x$ so $\Phi(x)=P(X_1<4X_2)$. I know that this question should be solved by standardizing a new variable $X_1-4X_2$ but it isn't giving me any progress because I always get to an integration that I don't know to calculate. Any help?