Y=0.4x^2-3x+1

Solution for Y=0.4x^2-3x+1 equation:

=0.4Y^2-3Y+1

We move all terms to the left:

-(0.4Y^2-3Y+1)=0

We get rid of parentheses

-0.4Y^2+3Y-1=0

a = -0.4; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·(-0.4)·(-1)
Δ = 7.4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{7.4}}{2*-0.4}=\frac{-3-\sqrt{7.4}}{-0.8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{7.4}}{2*-0.4}=\frac{-3+\sqrt{7.4}}{-0.8}
$