X/25x+2=53x-3

Solution for X/25x+2=53x-3 equation:

X/25X+2=53X-3

We move all terms to the left:

X/25X+2-(53X-3)=0


Domain of the equation: 25X!=0

X!=0/25

X!=0

X∈R


We get rid of parentheses

X/25X-53X+3+2=0

We multiply all the terms by the denominator


X-53X*25X+3*25X+2*25X=0

Wy multiply elements

-1325X^2+X+75X+50X=0

We add all the numbers together, and all the variables

-1325X^2+126X=0

a = -1325; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·(-1325)·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*-1325}=\frac{-252}{-2650}
=126/1325
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*-1325}=\frac{0}{-2650}
=0
$