4x+54=x2

Solution for 4x+54=x2 equation:

4x+54=x2

We move all terms to the left:

4x+54-(x2)=0

We add all the numbers together, and all the variables

-1x^2+4x+54=0

a = -1; b = 4; c = +54;
Δ = b2-4ac
Δ = 42-4·(-1)·54
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{58}}{2*-1}=\frac{-4-2\sqrt{58}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{58}}{2*-1}=\frac{-4+2\sqrt{58}}{-2}
$