Y=21x^2-46x+24

Solution for Y=21x^2-46x+24 equation:

=21Y^2-46Y+24

We move all terms to the left:

-(21Y^2-46Y+24)=0

We get rid of parentheses

-21Y^2+46Y-24=0

a = -21; b = 46; c = -24;
Δ = b2-4ac
Δ = 462-4·(-21)·(-24)
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{-(46)-10}{2*-21}=\frac{-56}{-42}
=1+1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+10}{2*-21}=\frac{-36}{-42}
=6/7
$