2x+5=1/25x+3

Solution for 2x+5=1/25x+3 equation:

2x+5=1/25x+3

We move all terms to the left:

2x+5-(1/25x+3)=0


Domain of the equation: 25x+3)!=0

x∈R


We get rid of parentheses

2x-1/25x-3+5=0

We multiply all the terms by the denominator


2x*25x-3*25x+5*25x-1=0

Wy multiply elements

50x^2-75x+125x-1=0

We add all the numbers together, and all the variables

50x^2+50x-1=0

a = 50; b = 50; c = -1;
Δ = b2-4ac
Δ = 502-4·50·(-1)
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-30\sqrt{3}}{2*50}=\frac{-50-30\sqrt{3}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+30\sqrt{3}}{2*50}=\frac{-50+30\sqrt{3}}{100}
$