First square both sides.
(7x-5)+(15x+4)+ 2sqrt[(7x-5)(15x+4)]= 30x+31
22x-1 +2sqrt[(7x-5)(15x+4)]= 30x +31
sqrt[(7x-5)(15x+4)]= 4x + 16
Now square both sides again and solve the resulting quadratic.
Check my math; I tend to be sloppy.
Solve: sqrt(7x-5)+sqrt(15x+4)=sqrt(30x+31)
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