The Tschirnhaus Transform is a method to solve quartic equations. If the quartic equation has four distinct real roots, a low computation complexity algorithm is proposed and applied to the the 10-order Line Spectrum Pairs(LSP).However, during the procedures of calculation, the existence of the inverse trigonometric functions increase the computation load of the hardware implementation. We also propose some methods to solve this problem and increase the speed of the calculation. A table of comparison result with the previous proposed Complex-Free Farrari formula is also included.