3/5x+8=5/2x-11

Solution for 3/5x+8=5/2x-11 equation:

3/5x+8=5/2x-11

We move all terms to the left:

3/5x+8-(5/2x-11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-11)!=0

x∈R


We get rid of parentheses

3/5x-5/2x+11+8=0

We calculate fractions


6x/10x^2+(-25x)/10x^2+11+8=0

We add all the numbers together, and all the variables

6x/10x^2+(-25x)/10x^2+19=0

We multiply all the terms by the denominator


6x+(-25x)+19*10x^2=0

Wy multiply elements

190x^2+6x+(-25x)=0

We get rid of parentheses

190x^2+6x-25x=0

We add all the numbers together, and all the variables

190x^2-19x=0

a = 190; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·190·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*190}=\frac{0}{380}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*190}=\frac{38}{380}
=1/10
$