x=x2-4x-45

Solution for x=x2-4x-45 equation:

x=x2-4x-45

We move all terms to the left:

x-(x2-4x-45)=0

We add all the numbers together, and all the variables

-(+x^2-4x-45)+x=0

We get rid of parentheses

-x^2+4x+x+45=0

We add all the numbers together, and all the variables

-1x^2+5x+45=0

a = -1; b = 5; c = +45;
Δ = b2-4ac
Δ = 52-4·(-1)·45
Δ = 205
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{205}}{2*-1}=\frac{-5-\sqrt{205}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{205}}{2*-1}=\frac{-5+\sqrt{205}}{-2}
$