10/3x+25=5/2x-7

Solution for 10/3x+25=5/2x-7 equation:

10/3x+25=5/2x-7

We move all terms to the left:

10/3x+25-(5/2x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

10/3x-5/2x+7+25=0

We calculate fractions


20x/6x^2+(-15x)/6x^2+7+25=0

We add all the numbers together, and all the variables

20x/6x^2+(-15x)/6x^2+32=0

We multiply all the terms by the denominator


20x+(-15x)+32*6x^2=0

Wy multiply elements

192x^2+20x+(-15x)=0

We get rid of parentheses

192x^2+20x-15x=0

We add all the numbers together, and all the variables

192x^2+5x=0

a = 192; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·192·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*192}=\frac{-10}{384}
=-5/192
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*192}=\frac{0}{384}
=0
$