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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/10x^2+15x/10x^2-5-2=0

We add all the numbers together, and all the variables

6x/10x^2+15x/10x^2-7=0

We multiply all the terms by the denominator


6x+15x-7*10x^2=0

We add all the numbers together, and all the variables

21x-7*10x^2=0

Wy multiply elements

-70x^2+21x=0

a = -70; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-70)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-70}=\frac{-42}{-140}
=3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-70}=\frac{0}{-140}
=0
$