Y=21x^2-38x+16

Solution for Y=21x^2-38x+16 equation:

=21Y^2-38Y+16

We move all terms to the left:

-(21Y^2-38Y+16)=0

We get rid of parentheses

-21Y^2+38Y-16=0

a = -21; b = 38; c = -16;
Δ = b2-4ac
Δ = 382-4·(-21)·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-10}{2*-21}=\frac{-48}{-42}
=1+1/7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+10}{2*-21}=\frac{-28}{-42}
=2/3
$