9(x+5)*x+5=480

Solution for 9(x+5)*x+5=480 equation:

9(x+5)*x+5=480

We move all terms to the left:

9(x+5)*x+5-(480)=0

We add all the numbers together, and all the variables

9(x+5)*x-475=0

We multiply parentheses

9x^2+45x-475=0

a = 9; b = 45; c = -475;
Δ = b2-4ac
Δ = 452-4·9·(-475)
Δ = 19125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19125}=\sqrt{225*85}=\sqrt{225}*\sqrt{85}=15\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-15\sqrt{85}}{2*9}=\frac{-45-15\sqrt{85}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+15\sqrt{85}}{2*9}=\frac{-45+15\sqrt{85}}{18}
$