144=x(x+4)

Solution for 144=x(x+4) equation:

144=x(x+4)

We move all terms to the left:

144-(x(x+4))=0


We calculate terms in parentheses: -(x(x+4)), so:

x(x+4)

We multiply parentheses

x^2+4x

Back to the equation:

-(x^2+4x)


We get rid of parentheses

-x^2-4x+144=0

We add all the numbers together, and all the variables

-1x^2-4x+144=0

a = -1; b = -4; c = +144;
Δ = b2-4ac
Δ = -42-4·(-1)·144
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*-1}=\frac{4-4\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{37}}{2*-1}=\frac{4+4\sqrt{37}}{-2}
$