-40(x^2-20x+85)=x

Solution for -40(x^2-20x+85)=x equation:

-40(x^2-20x+85)=x

We move all terms to the left:

-40(x^2-20x+85)-(x)=0

We add all the numbers together, and all the variables

-1x-40(x^2-20x+85)=0

We multiply parentheses

-40x^2-1x+800x-3400=0

We add all the numbers together, and all the variables

-40x^2+799x-3400=0

a = -40; b = 799; c = -3400;
Δ = b2-4ac
Δ = 7992-4·(-40)·(-3400)
Δ = 94401
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:

$\sqrt{\Delta}=\sqrt{94401}=\sqrt{9*10489}=\sqrt{9}*\sqrt{10489}=3\sqrt{10489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(799)-3\sqrt{10489}}{2*-40}=\frac{-799-3\sqrt{10489}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(799)+3\sqrt{10489}}{2*-40}=\frac{-799+3\sqrt{10489}}{-80}
$