8(3-96x)=9+3x(54x+10)

Solution for 8(3-96x)=9+3x(54x+10) equation:

8(3-96x)=9+3x(54x+10)

We move all terms to the left:

8(3-96x)-(9+3x(54x+10))=0

We add all the numbers together, and all the variables

8(-96x+3)-(9+3x(54x+10))=0

We multiply parentheses

-768x-(9+3x(54x+10))+24=0


We calculate terms in parentheses: -(9+3x(54x+10)), so:

9+3x(54x+10)

determiningTheFunctionDomain
3x(54x+10)+9

We multiply parentheses

162x^2+30x+9

Back to the equation:

-(162x^2+30x+9)


We get rid of parentheses

-162x^2-768x-30x-9+24=0

We add all the numbers together, and all the variables

-162x^2-798x+15=0

a = -162; b = -798; c = +15;
Δ = b2-4ac
Δ = -7982-4·(-162)·15
Δ = 646524
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:

$\sqrt{\Delta}=\sqrt{646524}=\sqrt{36*17959}=\sqrt{36}*\sqrt{17959}=6\sqrt{17959}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-798)-6\sqrt{17959}}{2*-162}=\frac{798-6\sqrt{17959}}{-324}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-798)+6\sqrt{17959}}{2*-162}=\frac{798+6\sqrt{17959}}{-324}
$