2(518/49x)=784/101x

Solution for 2(518/49x)=784/101x equation:

2(518/49x)=784/101x

We move all terms to the left:

2(518/49x)-(784/101x)=0


Domain of the equation: 49x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 101x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(+518/49x)-(+784/101x)=0

We multiply parentheses

1036x-(+784/101x)=0

We get rid of parentheses

1036x-784/101x=0

We multiply all the terms by the denominator


1036x*101x-784=0

Wy multiply elements

104636x^2-784=0

a = 104636; b = 0; c = -784;
Δ = b2-4ac
Δ = 02-4·104636·(-784)
Δ = 328138496
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:

$\sqrt{\Delta}=\sqrt{328138496}=\sqrt{12544*26159}=\sqrt{12544}*\sqrt{26159}=112\sqrt{26159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-112\sqrt{26159}}{2*104636}=\frac{0-112\sqrt{26159}}{209272}
=-\frac{112\sqrt{26159}}{209272}
=-\frac{2\sqrt{26159}}{3737}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+112\sqrt{26159}}{2*104636}=\frac{0+112\sqrt{26159}}{209272}
=\frac{112\sqrt{26159}}{209272}
=\frac{2\sqrt{26159}}{3737}
$