X(x+10)+(1+30)+2x=360

Solution for X(x+10)+(1+30)+2x=360 equation:

X(X+10)+(1+30)+2X=360

We move all terms to the left:

X(X+10)+(1+30)+2X-(360)=0

determiningTheFunctionDomain
X(X+10)+2X-360+(1+30)=0

We add all the numbers together, and all the variables

X(X+10)+2X-360+31=0

We add all the numbers together, and all the variables

2X+X(X+10)-329=0

We multiply parentheses

X^2+2X+10X-329=0

We add all the numbers together, and all the variables

X^2+12X-329=0

a = 1; b = 12; c = -329;
Δ = b2-4ac
Δ = 122-4·1·(-329)
Δ = 1460
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1460}=\sqrt{4*365}=\sqrt{4}*\sqrt{365}=2\sqrt{365}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{365}}{2*1}=\frac{-12-2\sqrt{365}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{365}}{2*1}=\frac{-12+2\sqrt{365}}{2}
$