4000+5*q+10*q^2=5*q+20*q^2

Solution for 4000+5*q+10*q^2=5*q+20*q^2 equation:

4000+5q+10q^2=5q+20q^2

We move all terms to the left:

4000+5q+10q^2-(5q+20q^2)=0

We get rid of parentheses

10q^2-20q^2-5q+5q+4000=0

We add all the numbers together, and all the variables

-10q^2+4000=0

a = -10; b = 0; c = +4000;
Δ = b2-4ac
Δ = 02-4·(-10)·4000
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400}{2*-10}=\frac{-400}{-20}
=+20
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400}{2*-10}=\frac{400}{-20}
=-20
$