(2x-45)(2x-45)=(45*45)+(x*x)

Solution for (2x-45)(2x-45)=(45*45)+(x*x) equation:

(2x-45)(2x-45)=(45*45)+(x*x)

We move all terms to the left:

(2x-45)(2x-45)-((45*45)+(x*x))=0

We add all the numbers together, and all the variables

(2x-45)(2x-45)-(2025+(+x*x))=0

We multiply parentheses ..

(+4x^2-90x-90x+2025)-(2025+(+x*x))=0


We calculate terms in parentheses: -(2025+(+x*x)), so:

2025+(+x*x)

determiningTheFunctionDomain
(+x*x)+2025

We get rid of parentheses

x*x+2025

Wy multiply elements

x^2+2025

Back to the equation:

-(x^2+2025)


We get rid of parentheses

4x^2-x^2-90x-90x+2025-2025=0

We add all the numbers together, and all the variables

3x^2-180x=0

a = 3; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·3·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*3}=\frac{360}{6}
=60
$