x^2-40x=4=0

Solution for x^2-40x=4=0 equation:

x^2-40x=4=0

We move all terms to the left:

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

a = 1; b = -40; c = -4;
Δ = b2-4ac
Δ = -402-4·1·(-4)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{101}}{2*1}=\frac{40-4\sqrt{101}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{101}}{2*1}=\frac{40+4\sqrt{101}}{2}
$