9y+5y(22y+8)=500

Solution for 9y+5y(22y+8)=500 equation:

9y+5y(22y+8)=500

We move all terms to the left:

9y+5y(22y+8)-(500)=0

We multiply parentheses

110y^2+9y+40y-500=0

We add all the numbers together, and all the variables

110y^2+49y-500=0

a = 110; b = 49; c = -500;
Δ = b2-4ac
Δ = 492-4·110·(-500)
Δ = 222401
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{-(49)-\sqrt{222401}}{2*110}=\frac{-49-\sqrt{222401}}{220}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{222401}}{2*110}=\frac{-49+\sqrt{222401}}{220}
$