Y=2x^2-6.5x+3.2

Solution for Y=2x^2-6.5x+3.2 equation:

=2Y^2-6.5Y+3.2

We move all terms to the left:

-(2Y^2-6.5Y+3.2)=0

We get rid of parentheses

-2Y^2+6.5Y-3.2=0

a = -2; b = 6.5; c = -3.2;
Δ = b2-4ac
Δ = 6.52-4·(-2)·(-3.2)
Δ = 16.65
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{-(6.5)-\sqrt{16.65}}{2*-2}=\frac{-6.5-\sqrt{16.65}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.5)+\sqrt{16.65}}{2*-2}=\frac{-6.5+\sqrt{16.65}}{-4}
$