-3/5x+3=1/2x-5

Solution for -3/5x+3=1/2x-5 equation:

-3/5x+3=1/2x-5

We move all terms to the left:

-3/5x+3-(1/2x-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-1/2x+5+3=0

We calculate fractions


(-6x)/10x^2+(-5x)/10x^2+5+3=0

We add all the numbers together, and all the variables

(-6x)/10x^2+(-5x)/10x^2+8=0

We multiply all the terms by the denominator


(-6x)+(-5x)+8*10x^2=0

Wy multiply elements

80x^2+(-6x)+(-5x)=0

We get rid of parentheses

80x^2-6x-5x=0

We add all the numbers together, and all the variables

80x^2-11x=0

a = 80; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·80·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*80}=\frac{0}{160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*80}=\frac{22}{160}
=11/80
$