^ { 8 } P _ { 5 } = 7 P _ { 5 } + K ^ { 7 } P _ { 4 }
Solve for K
K=-\frac{P_{5}}{120}+8
Solve for P_5
P_{5}=960-120K
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7P_{5}+Kpermutation(7,4)=permutation(8,5)
Swap sides so that all variable terms are on the left hand side.
Kpermutation(7,4)=permutation(8,5)-7P_{5}
Subtract 7P_{5} from both sides.
840K=6720-7P_{5}
The equation is in standard form.
\frac{840K}{840}=\frac{6720-7P_{5}}{840}
Divide both sides by 840.
K=\frac{6720-7P_{5}}{840}
Dividing by 840 undoes the multiplication by 840.
K=-\frac{P_{5}}{120}+8
Divide 6720-7P_{5} by 840.
7P_{5}+Kpermutation(7,4)=permutation(8,5)
Swap sides so that all variable terms are on the left hand side.
7P_{5}=permutation(8,5)-Kpermutation(7,4)
Subtract Kpermutation(7,4) from both sides.
7P_{5}=-Kpermutation(7,4)+permutation(8,5)
Reorder the terms.
7P_{5}=6720-840K
The equation is in standard form.
\frac{7P_{5}}{7}=\frac{6720-840K}{7}
Divide both sides by 7.
P_{5}=\frac{6720-840K}{7}
Dividing by 7 undoes the multiplication by 7.
P_{5}=960-120K
Divide 6720-840K by 7.
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