(19/1334)x-(383/24)=3675

Solution for (19/1334)x-(383/24)=3675 equation:

(19/1334)x-(383/24)=3675

We move all terms to the left:

(19/1334)x-(383/24)-(3675)=0


Domain of the equation: 1334)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(19/1334)x-3675-(383/24)=0

We add all the numbers together, and all the variables

(+19/1334)x-3675-(+383/24)=0

We multiply parentheses

19x^2-3675-(+383/24)=0

We get rid of parentheses

19x^2-3675-383/24=0

We multiply all the terms by the denominator


19x^2*24-383-3675*24=0

We add all the numbers together, and all the variables

19x^2*24-88583=0

Wy multiply elements

456x^2-88583=0

a = 456; b = 0; c = -88583;
Δ = b2-4ac
Δ = 02-4·456·(-88583)
Δ = 161575392
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:

$\sqrt{\Delta}=\sqrt{161575392}=\sqrt{16*10098462}=\sqrt{16}*\sqrt{10098462}=4\sqrt{10098462}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10098462}}{2*456}=\frac{0-4\sqrt{10098462}}{912}
=-\frac{4\sqrt{10098462}}{912}
=-\frac{\sqrt{10098462}}{228}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10098462}}{2*456}=\frac{0+4\sqrt{10098462}}{912}
=\frac{4\sqrt{10098462}}{912}
=\frac{\sqrt{10098462}}{228}
$