X(x+3)+x(8+x)=37

Solution for X(x+3)+x(8+x)=37 equation:

X(X+3)+X(8+X)=37

We move all terms to the left:

X(X+3)+X(8+X)-(37)=0

We add all the numbers together, and all the variables

X(X+3)+X(X+8)-37=0

We multiply parentheses

X^2+X^2+3X+8X-37=0

We add all the numbers together, and all the variables

2X^2+11X-37=0

a = 2; b = 11; c = -37;
Δ = b2-4ac
Δ = 112-4·2·(-37)
Δ = 417
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{-(11)-\sqrt{417}}{2*2}=\frac{-11-\sqrt{417}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{417}}{2*2}=\frac{-11+\sqrt{417}}{4}
$