x(x+9)=4(9)

Solution for x(x+9)=4(9) equation:

x(x+9)=4(9)

We move all terms to the left:

x(x+9)-(4(9))=0

determiningTheFunctionDomain
x(x+9)-49=0

We multiply parentheses

x^2+9x-49=0

a = 1; b = 9; c = -49;
Δ = b2-4ac
Δ = 92-4·1·(-49)
Δ = 277
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{-(9)-\sqrt{277}}{2*1}=\frac{-9-\sqrt{277}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{277}}{2*1}=\frac{-9+\sqrt{277}}{2}
$