0=40x+7x^2

Solution for 0=40x+7x^2 equation:

0=40x+7x^2

We move all terms to the left:

0-(40x+7x^2)=0

We add all the numbers together, and all the variables

-(40x+7x^2)=0

We get rid of parentheses

-7x^2-40x=0

a = -7; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·(-7)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*-7}=\frac{80}{-14}
=-5+5/7
$