x2-4x=86

Solution for x2-4x=86 equation:

x2-4x=86

We move all terms to the left:

x2-4x-(86)=0

We add all the numbers together, and all the variables

x^2-4x-86=0

a = 1; b = -4; c = -86;
Δ = b2-4ac
Δ = -42-4·1·(-86)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{10}}{2*1}=\frac{4-6\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{10}}{2*1}=\frac{4+6\sqrt{10}}{2}
$