40-4x-4x+0.4(x^2)-(x^2)=0

Solution for 40-4x-4x+0.4(x^2)-(x^2)=0 equation:

40-4x-4x+0.4(x^2)-(x^2)=0

determiningTheFunctionDomain
0.4x^2-x^2-4x-4x+40=0

We add all the numbers together, and all the variables

-0.6x^2-8x+40=0

a = -0.6; b = -8; c = +40;
Δ = b2-4ac
Δ = -82-4·(-0.6)·40
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*-0.6}=\frac{8-4\sqrt{10}}{-1.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*-0.6}=\frac{8+4\sqrt{10}}{-1.2}
$