X^2-4x=164

Solution for X^2-4x=164 equation:

X^2-4X=164

We move all terms to the left:

X^2-4X-(164)=0

a = 1; b = -4; c = -164;
Δ = b2-4ac
Δ = -42-4·1·(-164)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{42}}{2*1}=\frac{4-4\sqrt{42}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{42}}{2*1}=\frac{4+4\sqrt{42}}{2}
$