(382/24)x=114/23

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

(382/24)x=114/23

We move all terms to the left:

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


Domain of the equation: 24)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

382x^2-(+114/23)=0

We get rid of parentheses

382x^2-114/23=0

We multiply all the terms by the denominator


382x^2*23-114=0

Wy multiply elements

8786x^2-114=0

a = 8786; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·8786·(-114)
Δ = 4006416
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:

$\sqrt{\Delta}=\sqrt{4006416}=\sqrt{16*250401}=\sqrt{16}*\sqrt{250401}=4\sqrt{250401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{250401}}{2*8786}=\frac{0-4\sqrt{250401}}{17572}
=-\frac{4\sqrt{250401}}{17572}
=-\frac{\sqrt{250401}}{4393}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{250401}}{2*8786}=\frac{0+4\sqrt{250401}}{17572}
=\frac{4\sqrt{250401}}{17572}
=\frac{\sqrt{250401}}{4393}
$