144+3x=x(x-3)

Solution for 144+3x=x(x-3) equation:

144+3x=x(x-3)

We move all terms to the left:

144+3x-(x(x-3))=0


We calculate terms in parentheses: -(x(x-3)), so:

x(x-3)

We multiply parentheses

x^2-3x

Back to the equation:

-(x^2-3x)


We get rid of parentheses

-x^2+3x+3x+144=0

We add all the numbers together, and all the variables

-1x^2+6x+144=0

a = -1; b = 6; c = +144;
Δ = b2-4ac
Δ = 62-4·(-1)·144
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{17}}{2*-1}=\frac{-6-6\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{17}}{2*-1}=\frac{-6+6\sqrt{17}}{-2}
$