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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2736x^2-88200x+382=0

a = 2736; b = -88200; c = +382;
Δ = b2-4ac
Δ = -882002-4·2736·382
Δ = 7775059392
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:

$\sqrt{\Delta}=\sqrt{7775059392}=\sqrt{576*13498367}=\sqrt{576}*\sqrt{13498367}=24\sqrt{13498367}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88200)-24\sqrt{13498367}}{2*2736}=\frac{88200-24\sqrt{13498367}}{5472}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88200)+24\sqrt{13498367}}{2*2736}=\frac{88200+24\sqrt{13498367}}{5472}
$