240=q(70-5q)

Solution for 240=q(70-5q) equation:

240=q(70-5q)

We move all terms to the left:

240-(q(70-5q))=0

We add all the numbers together, and all the variables

-(q(-5q+70))+240=0


We calculate terms in parentheses: -(q(-5q+70)), so:

q(-5q+70)

We multiply parentheses

-5q^2+70q

Back to the equation:

-(-5q^2+70q)


We get rid of parentheses

5q^2-70q+240=0

a = 5; b = -70; c = +240;
Δ = b2-4ac
Δ = -702-4·5·240
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10}{2*5}=\frac{60}{10}
=6
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10}{2*5}=\frac{80}{10}
=8
$