(3x-9)+x(x+28)=184

Solution for (3x-9)+x(x+28)=184 equation:

(3x-9)+x(x+28)=184

We move all terms to the left:

(3x-9)+x(x+28)-(184)=0

We multiply parentheses

x^2+(3x-9)+28x-184=0

We get rid of parentheses

x^2+3x+28x-9-184=0

We add all the numbers together, and all the variables

x^2+31x-193=0

a = 1; b = 31; c = -193;
Δ = b2-4ac
Δ = 312-4·1·(-193)
Δ = 1733
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{-(31)-\sqrt{1733}}{2*1}=\frac{-31-\sqrt{1733}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{1733}}{2*1}=\frac{-31+\sqrt{1733}}{2}
$