(x)+(x+1)(x+2)=72

Solution for (x)+(x+1)(x+2)=72 equation:

(x)+(x+1)(x+2)=72

We move all terms to the left:

(x)+(x+1)(x+2)-(72)=0

We multiply parentheses ..

(+x^2+2x+x+2)+x-72=0

We get rid of parentheses

x^2+2x+x+x+2-72=0

We add all the numbers together, and all the variables

x^2+4x-70=0

a = 1; b = 4; c = -70;
Δ = b2-4ac
Δ = 42-4·1·(-70)
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{74}}{2*1}=\frac{-4-2\sqrt{74}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{74}}{2*1}=\frac{-4+2\sqrt{74}}{2}
$