Y=2x^2-17x+21

Solution for Y=2x^2-17x+21 equation:

=2Y^2-17Y+21

We move all terms to the left:

-(2Y^2-17Y+21)=0

We get rid of parentheses

-2Y^2+17Y-21=0

a = -2; b = 17; c = -21;
Δ = b2-4ac
Δ = 172-4·(-2)·(-21)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-11}{2*-2}=\frac{-28}{-4}
=+7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+11}{2*-2}=\frac{-6}{-4}
=1+1/2
$