2x+x(x-3)=23

Solution for 2x+x(x-3)=23 equation:

2x+x(x-3)=23

We move all terms to the left:

2x+x(x-3)-(23)=0

We multiply parentheses

x^2+2x-3x-23=0

We add all the numbers together, and all the variables

x^2-1x-23=0

a = 1; b = -1; c = -23;
Δ = b2-4ac
Δ = -12-4·1·(-23)
Δ = 93
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{-(-1)-\sqrt{93}}{2*1}=\frac{1-\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{93}}{2*1}=\frac{1+\sqrt{93}}{2}
$