2x^2-40x=40+200

Solution for 2x^2-40x=40+200 equation:

2x^2-40x=40+200

We move all terms to the left:

2x^2-40x-(40+200)=0

We add all the numbers together, and all the variables

2x^2-40x-240=0

a = 2; b = -40; c = -240;
Δ = b2-4ac
Δ = -402-4·2·(-240)
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{55}}{2*2}=\frac{40-8\sqrt{55}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{55}}{2*2}=\frac{40+8\sqrt{55}}{4}
$