1441.sagews

var('E1 E2 E3 R1 R2 R3 I1 I2 I3')
solve( [E1-I1*R1-I3*R3==0,E2-I2*R2-I3*R3==0,I1+I2==I3], [I1,I2,I3])

[[I1 == ((E1 - E2)*R3 + E1*R2)/((R1 + R2)*R3 + R1*R2), I2 == -((E1 - E2)*R3 - E2*R1)/((R1 + R2)*R3 + R1*R2), I3 == (E1*R2 + E2*R1)/((R1 + R2)*R3 + R1*R2)]]

E1 = 20
E2 = 15
R1 = 36.5
R2=30.3
R3=58.1
solve( [E1-I1*R1-I3*R3==0,E2-I2*R2-I3*R3==0,I1+I2==I3], [I1,I2,I3])

[[I1 == (89650/498703), I2 == (25700/498703), I3 == (115350/498703)]]

float(89650/498703)

0.179766313818044

float(25700/498703)

0.051533678361670172

float(115350/498703)

0.23129999217971417