My new computer plays league worse than my last one...

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So I recently got a new laptop, and the first thing that I did was download league again. Unfortunately, it plays league 100 times worse than my last one. Even with game booster, I get 20 fps on lowest graphics.
Can anyone help me?

Manufacturer TOSHIBA
Model Satellite C855D
Total amount of system memory 4.00 GB RAM
System type 64-bit operating system
Number of processor cores 2


Display adapter type AMD Radeon HD 6300 series Graphics
Total available graphics memory 1967 MB
Dedicated graphics memory 384 MB
Dedicated system memory 0 MB
Shared system memory 1583 MB
Display adapter driver version 8.982.7.0
Primary monitor resolution 1360x768
DirectX version DirectX 11 or better