5x+3/252x-3=50

Solution for 5x+3/252x-3=50 equation:

5x+3/252x-3=50

We move all terms to the left:

5x+3/252x-3-(50)=0


Domain of the equation: 252x!=0

x!=0/252

x!=0

x∈R


We add all the numbers together, and all the variables

5x+3/252x-53=0

We multiply all the terms by the denominator


5x*252x-53*252x+3=0

Wy multiply elements

1260x^2-13356x+3=0

a = 1260; b = -13356; c = +3;
Δ = b2-4ac
Δ = -133562-4·1260·3
Δ = 178367616
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:

$\sqrt{\Delta}=\sqrt{178367616}=\sqrt{576*309666}=\sqrt{576}*\sqrt{309666}=24\sqrt{309666}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13356)-24\sqrt{309666}}{2*1260}=\frac{13356-24\sqrt{309666}}{2520}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13356)+24\sqrt{309666}}{2*1260}=\frac{13356+24\sqrt{309666}}{2520}
$