There is no variable c in the equations provided by you.
If it has to be determined whether y = 3x + 4 is a tangent to y = 4x^2- 3x + 8, the equation 3x + 4 = 4x^2- 3x + 8 should have only one solution.
3x + 4 = 4x^2- 3x + 8
=> 4x^2 - 6x + 4 = 0
When a quadratic equation ax^2 + bx + c = 0 has one common root, the determinant b^2 - 4ac = 0
Here, a = 4, b = -6 and c = 4
b^2 - 4ac = 36 - 64 = -28
As the equation has more than one root, the line y = 3x + 4 is a intersects the curve y = 4x^2- 3x + 8 at more than one point.
The line y = 3x + 4 is not a tangent to y = 4x^2- 3x + 8