(382/24)-(114/23)*x-(3675x)=92+53

Solution for (382/24)-(114/23)*x-(3675x)=92+53 equation:

(382/24)-(114/23)*x-(3675x)=92+53

We move all terms to the left:

(382/24)-(114/23)*x-(3675x)-(92+53)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+114/23)*x-3675x+(+382/24)-145=0

We add all the numbers together, and all the variables

-3675x-(+114/23)*x-145+(+382/24)=0

We multiply parentheses

-114x^2-3675x-145+(+382/24)=0

We get rid of parentheses

-114x^2-3675x-145+382/24=0

We multiply all the terms by the denominator


-114x^2*24-3675x*24+382-145*24=0

We add all the numbers together, and all the variables

-114x^2*24-3675x*24-3098=0

Wy multiply elements

-2736x^2-88200x-3098=0

a = -2736; b = -88200; c = -3098;
Δ = b2-4ac
Δ = -882002-4·(-2736)·(-3098)
Δ = 7745335488
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:

$\sqrt{\Delta}=\sqrt{7745335488}=\sqrt{576*13446763}=\sqrt{576}*\sqrt{13446763}=24\sqrt{13446763}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88200)-24\sqrt{13446763}}{2*-2736}=\frac{88200-24\sqrt{13446763}}{-5472}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88200)+24\sqrt{13446763}}{2*-2736}=\frac{88200+24\sqrt{13446763}}{-5472}
$