x*(x+45)=27*(27+23)

Solution for x*(x+45)=27*(27+23) equation:

x(x+45)=27(27+23)

We move all terms to the left:

x(x+45)-(27(27+23))=0

We add all the numbers together, and all the variables

x(x+45)-(2750)=0

We add all the numbers together, and all the variables

x(x+45)-2750=0

We multiply parentheses

x^2+45x-2750=0

a = 1; b = 45; c = -2750;
Δ = b2-4ac
Δ = 452-4·1·(-2750)
Δ = 13025
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:

$\sqrt{\Delta}=\sqrt{13025}=\sqrt{25*521}=\sqrt{25}*\sqrt{521}=5\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{521}}{2*1}=\frac{-45-5\sqrt{521}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{521}}{2*1}=\frac{-45+5\sqrt{521}}{2}
$