40-40x=8-4x-7x^2

Solution for 40-40x=8-4x-7x^2 equation:

40-40x=8-4x-7x^2

We move all terms to the left:

40-40x-(8-4x-7x^2)=0

We get rid of parentheses

7x^2+4x-40x-8+40=0

We add all the numbers together, and all the variables

7x^2-36x+32=0

a = 7; b = -36; c = +32;
Δ = b2-4ac
Δ = -362-4·7·32
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-20}{2*7}=\frac{16}{14}
=1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+20}{2*7}=\frac{56}{14}
=4
$