3r^2 + 4r = -5
3r^2 + 4r + 5 = 0
this doesn't factor nicely, so quadratic formula
If ax^2 + bx + c = 0 then x = (-b +- sqrt(b^2-4ac) )/2a
r = (-4 +- sqrt(4^2 - 4(3)(5) )/2(3)
r = (-4 +- sqrt(16 - 60) )/6
r = (-4 +- sqrt(-44) )/6
You can't take the square root of a negative number, so there is no solution.
No value of r will make 3r^2 + 4r = -5 true.