4x+81=x2

Solution for 4x+81=x2 equation:

4x+81=x2

We move all terms to the left:

4x+81-(x2)=0

We add all the numbers together, and all the variables

-1x^2+4x+81=0

a = -1; b = 4; c = +81;
Δ = b2-4ac
Δ = 42-4·(-1)·81
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{85}}{2*-1}=\frac{-4-2\sqrt{85}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{85}}{2*-1}=\frac{-4+2\sqrt{85}}{-2}
$