24+4x=x(x+1)

Solution for 24+4x=x(x+1) equation:

24+4x=x(x+1)

We move all terms to the left:

24+4x-(x(x+1))=0


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

x(x+1)

We multiply parentheses

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2+4x-x+24=0

We add all the numbers together, and all the variables

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

a = -1; b = 3; c = +24;
Δ = b2-4ac
Δ = 32-4·(-1)·24
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{105}}{2*-1}=\frac{-3-\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-1}=\frac{-3+\sqrt{105}}{-2}
$