24=(x+8)(2.25-8/x)

Solution for 24=(x+8)(2.25-8/x) equation:

24=(x+8)(2.25-8/x)

We move all terms to the left:

24-((x+8)(2.25-8/x))=0


Domain of the equation: x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-((x+8)(-8/x+2.25))+24=0

We multiply parentheses ..

-((-8x^2+2.25x-64x+18))+24=0


We calculate terms in parentheses: -((-8x^2+2.25x-64x+18)), so:

(-8x^2+2.25x-64x+18)

We get rid of parentheses

-8x^2+2.25x-64x+18

We add all the numbers together, and all the variables

-8x^2-61.75x+18

Back to the equation:

-(-8x^2-61.75x+18)


We get rid of parentheses

8x^2+61.75x-18+24=0

We add all the numbers together, and all the variables

8x^2+61.75x+6=0

a = 8; b = 61.75; c = +6;
Δ = b2-4ac
Δ = 61.752-4·8·6
Δ = 3621.0625
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{-(61.75)-\sqrt{3621.0625}}{2*8}=\frac{-61.75-\sqrt{3621.0625}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61.75)+\sqrt{3621.0625}}{2*8}=\frac{-61.75+\sqrt{3621.0625}}{16}
$