400q2=20q-q2

Solution for 400q2=20q-q2 equation:

400q^2=20q-q2

We move all terms to the left:

400q^2-(20q-q2)=0

We add all the numbers together, and all the variables

400q^2-(+20q-1q^2)=0

We get rid of parentheses

400q^2+1q^2-20q=0

We add all the numbers together, and all the variables

401q^2-20q=0

a = 401; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·401·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*401}=\frac{0}{802}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*401}=\frac{40}{802}
=20/401
$