5x+3=125/25x

Solution for 5x+3=125/25x equation:

5x+3=125/25x

We move all terms to the left:

5x+3-(125/25x)=0


Domain of the equation: 25x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+125/25x)+3=0

We get rid of parentheses

5x-125/25x+3=0

We multiply all the terms by the denominator


5x*25x+3*25x-125=0

Wy multiply elements

125x^2+75x-125=0

a = 125; b = 75; c = -125;
Δ = b2-4ac
Δ = 752-4·125·(-125)
Δ = 68125
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:

$\sqrt{\Delta}=\sqrt{68125}=\sqrt{625*109}=\sqrt{625}*\sqrt{109}=25\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-25\sqrt{109}}{2*125}=\frac{-75-25\sqrt{109}}{250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+25\sqrt{109}}{2*125}=\frac{-75+25\sqrt{109}}{250}
$