180=113+x(x+5)

Solution for 180=113+x(x+5) equation:

180=113+x(x+5)

We move all terms to the left:

180-(113+x(x+5))=0


We calculate terms in parentheses: -(113+x(x+5)), so:

113+x(x+5)

determiningTheFunctionDomain
x(x+5)+113

We multiply parentheses

x^2+5x+113

Back to the equation:

-(x^2+5x+113)


We get rid of parentheses

-x^2-5x-113+180=0

We add all the numbers together, and all the variables

-1x^2-5x+67=0

a = -1; b = -5; c = +67;
Δ = b2-4ac
Δ = -52-4·(-1)·67
Δ = 293
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{293}}{2*-1}=\frac{5-\sqrt{293}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{293}}{2*-1}=\frac{5+\sqrt{293}}{-2}
$