180=65+x(x-5)

Solution for 180=65+x(x-5) equation:

180=65+x(x-5)

We move all terms to the left:

180-(65+x(x-5))=0


We calculate terms in parentheses: -(65+x(x-5)), so:

65+x(x-5)

determiningTheFunctionDomain
x(x-5)+65

We multiply parentheses

x^2-5x+65

Back to the equation:

-(x^2-5x+65)


We get rid of parentheses

-x^2+5x-65+180=0

We add all the numbers together, and all the variables

-1x^2+5x+115=0

a = -1; b = 5; c = +115;
Δ = b2-4ac
Δ = 52-4·(-1)·115
Δ = 485
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{485}}{2*-1}=\frac{-5-\sqrt{485}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{485}}{2*-1}=\frac{-5+\sqrt{485}}{-2}
$