Y=8x^2+59x+21

Solution for Y=8x^2+59x+21 equation:

=8Y^2+59Y+21

We move all terms to the left:

-(8Y^2+59Y+21)=0

We get rid of parentheses

-8Y^2-59Y-21=0

a = -8; b = -59; c = -21;
Δ = b2-4ac
Δ = -592-4·(-8)·(-21)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-53}{2*-8}=\frac{6}{-16}
=-3/8
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+53}{2*-8}=\frac{112}{-16}
=-7
$