Y=4n^2+11n+7

Solution for Y=4n^2+11n+7 equation:

=4Y^2+11Y+7

We move all terms to the left:

-(4Y^2+11Y+7)=0

We get rid of parentheses

-4Y^2-11Y-7=0

a = -4; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·(-4)·(-7)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*-4}=\frac{8}{-8}
=-1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*-4}=\frac{14}{-8}
=-1+3/4
$