(382/24)-(114/23)*x-(3675x)=92+35

Solution for (382/24)-(114/23)*x-(3675x)=92+35 equation:

(382/24)-(114/23)*x-(3675x)=92+35

We move all terms to the left:

(382/24)-(114/23)*x-(3675x)-(92+35)=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)-127=0

We add all the numbers together, and all the variables

-3675x-(+114/23)*x-127+(+382/24)=0

We multiply parentheses

-114x^2-3675x-127+(+382/24)=0

We get rid of parentheses

-114x^2-3675x-127+382/24=0

We multiply all the terms by the denominator


-114x^2*24-3675x*24+382-127*24=0

We add all the numbers together, and all the variables

-114x^2*24-3675x*24-2666=0

Wy multiply elements

-2736x^2-88200x-2666=0

a = -2736; b = -88200; c = -2666;
Δ = b2-4ac
Δ = -882002-4·(-2736)·(-2666)
Δ = 7750063296
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:

$\sqrt{\Delta}=\sqrt{7750063296}=\sqrt{576*13454971}=\sqrt{576}*\sqrt{13454971}=24\sqrt{13454971}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88200)-24\sqrt{13454971}}{2*-2736}=\frac{88200-24\sqrt{13454971}}{-5472}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88200)+24\sqrt{13454971}}{2*-2736}=\frac{88200+24\sqrt{13454971}}{-5472}
$