(8-2x*10-2x*x)=40

Solution for (8-2x*10-2x*x)=40 equation:

(8-2x*10-2x*x)=40

We move all terms to the left:

(8-2x*10-2x*x)-(40)=0

We add all the numbers together, and all the variables

(-2x*10-2x*x+8)-40=0

We get rid of parentheses

-2x*10-2x*x+8-40=0

We add all the numbers together, and all the variables

-2x*10-2x*x-32=0

Wy multiply elements

-2x^2-20x-32=0

a = -2; b = -20; c = -32;
Δ = b2-4ac
Δ = -202-4·(-2)·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12}{2*-2}=\frac{8}{-4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12}{2*-2}=\frac{32}{-4}
=-8
$