x(4+2.67x)=72

Solution for x(4+2.67x)=72 equation:

x(4+2.67x)=72

We move all terms to the left:

x(4+2.67x)-(72)=0

We add all the numbers together, and all the variables

x(2.67x+4)-72=0

We multiply parentheses

2x^2+4x-72=0

a = 2; b = 4; c = -72;
Δ = b2-4ac
Δ = 42-4·2·(-72)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{37}}{2*2}=\frac{-4-4\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{37}}{2*2}=\frac{-4+4\sqrt{37}}{4}
$