4/5x+27=5/3x-25

Solution for 4/5x+27=5/3x-25 equation:

4/5x+27=5/3x-25

We move all terms to the left:

4/5x+27-(5/3x-25)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

4/5x-5/3x+25+27=0

We calculate fractions


12x/15x^2+(-25x)/15x^2+25+27=0

We add all the numbers together, and all the variables

12x/15x^2+(-25x)/15x^2+52=0

We multiply all the terms by the denominator


12x+(-25x)+52*15x^2=0

Wy multiply elements

780x^2+12x+(-25x)=0

We get rid of parentheses

780x^2+12x-25x=0

We add all the numbers together, and all the variables

780x^2-13x=0

a = 780; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·780·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*780}=\frac{0}{1560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*780}=\frac{26}{1560}
=1/60
$