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Ev[shove] = (%call)(Ev[call]) + (%fold)(Ev[fold])
Ev = (0.90)([pot equity](total pot) - (amount shoved)) + (0.10)(6.85)
0 = (0.90)([X](20.10) - 7.75) + 0.685
0 = (0.90)(20.10X - 7.75) + 0.685
0 = 18.09X - 6.975 + 0.685
0 = 18.09X - 6.29
6.29 = 18.09X
X = 0.3477
So 34.77% equity needed with 10% fold equity. Also you only need around 38.6% equity to have a breakeven shove here if you know villain always calls.
If we assume villain has a range of something like (44,55,88+,76s, JcTc, QcJc, KcJc, KcQc, AcJc, AcTc, AcQc, etc) we would have the necessary 38.6% equity to shove with a range of (that would could reasonably 3bet with preflop):
QQ+, 8d8h, 8d8s, 8h8s, 5d5h, 5d5s, 5h5s, 4d4h, 4d4c, 4h4c, 76s, AcKc, AcQc, KcQc, AcJc, KcJc, QcJc, AcTc, KcTc, Ac9c, Kc9c, Ac7c, Kc7c, Qc7c, Jc7c, Tc7c, 9c7c, Ac6c, Kc6c, Qc6c, Jc6c, Tc6c, 9c6c, 8d5d, 8h5h, 8s5s, Ac4c, Kc4c, Qc4c, Jc4c, Tc4c, 9c4c, 8d4d, 8h4h, 7c4c, 6c4c, 5d4d, 5h4h, Ac3c, Kc3c, 7c3c, 6c3c, 4c3c, Ac2c, Kc2c, 7c2c, 6c2c, 4c2c, 3c2c
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