# Don't put me on hold...I need to talk to Vieta...wait...

**Algebra**Level 3

Consider the following:

Let \({ S }_{ 1 }\) be the sum of the roots of the equation \(4{ x }^{ 2 }+5-8x=0\)

Let \({ S }_{ 2 }\) be the sum of the roots of the equation \(\log _{ 6 }{ \left( x-2 \right) } +\log _{ 6 }{ \left( x+3 \right) } =2\)

Let \({ S }_{ 3 }\) be the sum of the roots of the equation \(x-\cfrac { 7 }{ x-3 } =3-\cfrac { 7 }{ x-3 } \)

Let \({ S }_{ 4 }\) be the sum of the roots of the equation \(4x+\sqrt { 2x } =1\)

Then find the value of \(Z\) where \(Z={ S }_{ 1 }+{ S }_{ 2 }+{ S }_{ 3 }+{ S }_{ 4 }\).