x(x+45)=27(27+50)

Solution for x(x+45)=27(27+50) equation:

x(x+45)=27(27+50)

We move all terms to the left:

x(x+45)-(27(27+50))=0

We add all the numbers together, and all the variables

x(x+45)-(2777)=0

We add all the numbers together, and all the variables

x(x+45)-2777=0

We multiply parentheses

x^2+45x-2777=0

a = 1; b = 45; c = -2777;
Δ = b2-4ac
Δ = 452-4·1·(-2777)
Δ = 13133
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{-(45)-\sqrt{13133}}{2*1}=\frac{-45-\sqrt{13133}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{13133}}{2*1}=\frac{-45+\sqrt{13133}}{2}
$