540=x+(x-45)x+(x-45)(x-45)

Solution for 540=x+(x-45)x+(x-45)(x-45) equation:

540=x+(x-45)x+(x-45)(x-45)

We move all terms to the left:

540-(x+(x-45)x+(x-45)(x-45))=0

We multiply parentheses ..

-(x+(x-45)x+(+x^2-45x-45x+2025))+540=0


We calculate terms in parentheses: -(x+(x-45)x+(+x^2-45x-45x+2025)), so:

x+(x-45)x+(+x^2-45x-45x+2025)

determiningTheFunctionDomain
(+x^2-45x-45x+2025)+x+(x-45)x

We multiply parentheses

(+x^2-45x-45x+2025)+x^2+x-45x

We get rid of parentheses

x^2+x^2-45x-45x+x-45x+2025

We add all the numbers together, and all the variables

2x^2-134x+2025

Back to the equation:

-(2x^2-134x+2025)


We get rid of parentheses

-2x^2+134x-2025+540=0

We add all the numbers together, and all the variables

-2x^2+134x-1485=0

a = -2; b = 134; c = -1485;
Δ = b2-4ac
Δ = 1342-4·(-2)·(-1485)
Δ = 6076
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:

$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(134)-14\sqrt{31}}{2*-2}=\frac{-134-14\sqrt{31}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(134)+14\sqrt{31}}{2*-2}=\frac{-134+14\sqrt{31}}{-4}
$