8/x+5=7/5x+25

Solution for 8/x+5=7/5x+25 equation:

8/x+5=7/5x+25

We move all terms to the left:

8/x+5-(7/5x+25)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+25)!=0

x∈R


We get rid of parentheses

8/x-7/5x-25+5=0

We calculate fractions


40x/5x^2+(-7x)/5x^2-25+5=0

We add all the numbers together, and all the variables

40x/5x^2+(-7x)/5x^2-20=0

We multiply all the terms by the denominator


40x+(-7x)-20*5x^2=0

Wy multiply elements

-100x^2+40x+(-7x)=0

We get rid of parentheses

-100x^2+40x-7x=0

We add all the numbers together, and all the variables

-100x^2+33x=0

a = -100; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-100)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-100}=\frac{-66}{-200}
=33/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-100}=\frac{0}{-200}
=0
$