440=90x+5x^2

Solution for 440=90x+5x^2 equation:

440=90x+5x^2

We move all terms to the left:

440-(90x+5x^2)=0

We get rid of parentheses

-5x^2-90x+440=0

a = -5; b = -90; c = +440;
Δ = b2-4ac
Δ = -902-4·(-5)·440
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-130}{2*-5}=\frac{-40}{-10}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+130}{2*-5}=\frac{220}{-10}
=-22
$