Y=42x^2-97x+56

Solution for Y=42x^2-97x+56 equation:

=42Y^2-97Y+56

We move all terms to the left:

-(42Y^2-97Y+56)=0

We get rid of parentheses

-42Y^2+97Y-56=0

a = -42; b = 97; c = -56;
Δ = b2-4ac
Δ = 972-4·(-42)·(-56)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(97)-1}{2*-42}=\frac{-98}{-84}
=1+1/6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+1}{2*-42}=\frac{-96}{-84}
=1+1/7
$