X+3x(x+3)=23

Solution for X+3x(x+3)=23 equation:

X+3X(X+3)=23

We move all terms to the left:

X+3X(X+3)-(23)=0

We multiply parentheses

3X^2+X+9X-23=0

We add all the numbers together, and all the variables

3X^2+10X-23=0

a = 3; b = 10; c = -23;
Δ = b2-4ac
Δ = 102-4·3·(-23)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{94}}{2*3}=\frac{-10-2\sqrt{94}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{94}}{2*3}=\frac{-10+2\sqrt{94}}{6}
$