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We investigate expected constraints on equilateral-type primordialnon-Gaussianities from future/ongoing imaging surveys, making use of the factthat they enhance the halo/galaxy bispectrum on large scales. As modelparameters to be constrained, in addition to $f_{\rm NL}^{\rm equil}$, which isrelated to the primordial bispectrum, we consider $g_{\rm NL}^{(\partial\sigma)^4}$, which is related to the primordial trispectrum that appeared inthe effective field theory of inflation. After calculating the angularbispectra of the halo/galaxy clustering and weak gravitational lensing based onthe integrated perturbation theory, we perform Fisher matrix analysis for threerepresentative surveys. We find that among the three surveys, the tightestconstraints come from Large Synoptic Survey Telescope ; its expected $1\sigma$errors on $f_{\rm NL}^{\rm equil}$ and $g_{\rm NL}^{(\partial \sigma)^4}$ arerespectively given by $7.0 \times 10^2$ and $4.9 \times 10^7$. Although thisconstraint is somewhat looser than the one from the current cosmic microwavebackground observation, since we obtain it independently, we can use thisconstraint as a cross check. We also evaluate the uncertainty with our resultscaused by using several approximations and discuss the possibility to obtaintighter constraint on $f_{\rm NL}^{\rm equil}$ and $g_{\rm NL}^{(\partial\sigma)^4}$.

Constraining equilateral-type primordial non-Gaussianities from imaging surveys