24=4x(10-x)

Solution for 24=4x(10-x) equation:

24=4x(10-x)

We move all terms to the left:

24-(4x(10-x))=0

We add all the numbers together, and all the variables

-(4x(-1x+10))+24=0


We calculate terms in parentheses: -(4x(-1x+10)), so:

4x(-1x+10)

We multiply parentheses

-4x^2+40x

Back to the equation:

-(-4x^2+40x)


We get rid of parentheses

4x^2-40x+24=0

a = 4; b = -40; c = +24;
Δ = b2-4ac
Δ = -402-4·4·24
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{19}}{2*4}=\frac{40-8\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{19}}{2*4}=\frac{40+8\sqrt{19}}{8}
$