x(x+3)+x=51

Solution for x(x+3)+x=51 equation:

x(x+3)+x=51

We move all terms to the left:

x(x+3)+x-(51)=0

We add all the numbers together, and all the variables

x+x(x+3)-51=0

We multiply parentheses

x^2+x+3x-51=0

We add all the numbers together, and all the variables

x^2+4x-51=0

a = 1; b = 4; c = -51;
Δ = b2-4ac
Δ = 42-4·1·(-51)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{55}}{2*1}=\frac{-4-2\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{55}}{2*1}=\frac{-4+2\sqrt{55}}{2}
$