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

Solution for (382/24)-(114/23)*x=0 equation:

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

We multiply parentheses

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

We get rid of parentheses

-114x^2+382/24=0

We multiply all the terms by the denominator


-114x^2*24+382=0

Wy multiply elements

-2736x^2+382=0

a = -2736; b = 0; c = +382;
Δ = b2-4ac
Δ = 02-4·(-2736)·382
Δ = 4180608
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:

$\sqrt{\Delta}=\sqrt{4180608}=\sqrt{576*7258}=\sqrt{576}*\sqrt{7258}=24\sqrt{7258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{7258}}{2*-2736}=\frac{0-24\sqrt{7258}}{-5472}
=-\frac{24\sqrt{7258}}{-5472}
=-\frac{\sqrt{7258}}{-228}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{7258}}{2*-2736}=\frac{0+24\sqrt{7258}}{-5472}
=\frac{24\sqrt{7258}}{-5472}
=\frac{\sqrt{7258}}{-228}
$