(382/24)-(114/23)*x-(3675x)=307

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Solution for (382/24)-(114/23)*x-(3675x)=307 equation: 



(382/24)-(114/23)*x-(3675x)=307

We move all terms to the left:

(382/24)-(114/23)*x-(3675x)-(307)=0



Domain of the equation: 23)*x!=0

x!=0/1

x!=0

x∈R



determiningTheFunctionDomain
-(114/23)*x-3675x-307+(382/24)=0

We add all the numbers together, and all the variables

-(+114/23)*x-3675x-307+(+382/24)=0

We add all the numbers together, and all the variables

-3675x-(+114/23)*x-307+(+382/24)=0

We multiply parentheses

-114x^2-3675x-307+(+382/24)=0

We get rid of parentheses

-114x^2-3675x-307+382/24=0

We multiply all the terms by the denominator


-114x^2*24-3675x*24+382-307*24=0

We add all the numbers together, and all the variables

-114x^2*24-3675x*24-6986=0

Wy multiply elements

-2736x^2-88200x-6986=0

a = -2736; b = -88200; c = -6986;
Δ = b2-4ac
Δ = -882002-4·(-2736)·(-6986)
Δ = 7702785216
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:


$\sqrt{\Delta}=\sqrt{7702785216}=\sqrt{576*13372891}=\sqrt{576}*\sqrt{13372891}=24\sqrt{13372891}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88200)-24\sqrt{13372891}}{2*-2736}=\frac{88200-24\sqrt{13372891}}{-5472}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88200)+24\sqrt{13372891}}{2*-2736}=\frac{88200+24\sqrt{13372891}}{-5472}
$

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