24=8x(2x+36)

Solution for 24=8x(2x+36) equation:

24=8x(2x+36)

We move all terms to the left:

24-(8x(2x+36))=0


We calculate terms in parentheses: -(8x(2x+36)), so:

8x(2x+36)

We multiply parentheses

16x^2+288x

Back to the equation:

-(16x^2+288x)


We get rid of parentheses

-16x^2-288x+24=0

a = -16; b = -288; c = +24;
Δ = b2-4ac
Δ = -2882-4·(-16)·24
Δ = 84480
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:

$\sqrt{\Delta}=\sqrt{84480}=\sqrt{256*330}=\sqrt{256}*\sqrt{330}=16\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-16\sqrt{330}}{2*-16}=\frac{288-16\sqrt{330}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+16\sqrt{330}}{2*-16}=\frac{288+16\sqrt{330}}{-32}
$