24=x(3x+1)

Solution for 24=x(3x+1) equation:

24=x(3x+1)

We move all terms to the left:

24-(x(3x+1))=0


We calculate terms in parentheses: -(x(3x+1)), so:

x(3x+1)

We multiply parentheses

3x^2+x

Back to the equation:

-(3x^2+x)


We get rid of parentheses

-3x^2-x+24=0

We add all the numbers together, and all the variables

-3x^2-1x+24=0

a = -3; b = -1; c = +24;
Δ = b2-4ac
Δ = -12-4·(-3)·24
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*-3}=\frac{18}{-6}
=-3
$