Y(x^2-81)=5x+6

Solution for Y(x^2-81)=5x+6 equation:

(Y^2-81)=5Y+6

We move all terms to the left:

(Y^2-81)-(5Y+6)=0

We get rid of parentheses

Y^2-5Y-81-6=0

We add all the numbers together, and all the variables

Y^2-5Y-87=0

a = 1; b = -5; c = -87;
Δ = b2-4ac
Δ = -52-4·1·(-87)
Δ = 373
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{373}}{2*1}=\frac{5-\sqrt{373}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{373}}{2*1}=\frac{5+\sqrt{373}}{2}
$