Consumer and producer surplus with integrals

[mathmathmath123]

The demand equation for a product is p=70- (60q/(sqroot q^2+3600)) and the supply equation is p=10 ln(q+20)-28. Determine the consumer's surplus and the producer's surplus under market equilibrium.
I know the formulas for consumer and producer surplus but I don't know how to rearrange these formulas to get the equilibrium quantity and price. Usually you must set the equations equal to each other and get the equilibrium value for q, then plug this value into the demand equation to get the equilibrium value for p, and then solve the integral formula accordingly.

 

[Deleted member 4993]

The demand equation for a product is p=70- (60q/(sqroot q^2+3600)) and the supply equation is p=10 ln(q+20)-28. Determine the consumer's surplus and the producer's surplus under market equilibrium.
I know the formulas for consumer and producer surplus but I don't know how to rearrange these formulas to get the equilibrium quantity and price. Usually you must set the equations equal to each other and get the equilibrium value for q, then plug this value into the demand equation to get the equilibrium value for p, and then solve the integral formula accordingly.

I have not worked it out - but at a first glance it looks like you need an numerical approximation method (e.g. Newton-Raphson) to calculate the equilibrium price.