5x^2-40x=200

Solution for 5x^2-40x=200 equation:

5x^2-40x=200

We move all terms to the left:

5x^2-40x-(200)=0

a = 5; b = -40; c = -200;
Δ = b2-4ac
Δ = -402-4·5·(-200)
Δ = 5600
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:

$\sqrt{\Delta}=\sqrt{5600}=\sqrt{400*14}=\sqrt{400}*\sqrt{14}=20\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{14}}{2*5}=\frac{40-20\sqrt{14}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{14}}{2*5}=\frac{40+20\sqrt{14}}{10}
$