Y=(6n2-19n-7)

Solution for Y=(6n2-19n-7) equation:

=(6Y^2-19Y-7)

We move all terms to the left:

-((6Y^2-19Y-7))=0


We calculate terms in parentheses: -((6Y^2-19Y-7)), so:

(6Y^2-19Y-7)

We get rid of parentheses

6Y^2-19Y-7

Back to the equation:

-(6Y^2-19Y-7)


We get rid of parentheses

-6Y^2+19Y+7=0

a = -6; b = 19; c = +7;
Δ = b2-4ac
Δ = 192-4·(-6)·7
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-23}{2*-6}=\frac{-42}{-12}
=3+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+23}{2*-6}=\frac{4}{-12}
=-1/3
$