Since y=f(x) is a linear equation, let y = mx+c.
2x^2 - 3x = y = mx + c which is equivalent to x^2+4x+3=0.
2x^2 - (3+m)x -c = 0
x^2 - (3+m)/2 x - c/2 = 0 should be identical to x^2+4x+3=0.
Comparing the coefficient,
- (3+m)/2 = 4
m = -11
-c/2 = 3
c = -6
Therefore y = -11x-6.