1/2x+3/5x-3=2/5x+4

Solution for 1/2x+3/5x-3=2/5x+4 equation:

1/2x+3/5x-3=2/5x+4

We move all terms to the left:

1/2x+3/5x-3-(2/5x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

1/2x+3/5x-2/5x-4-3=0

We calculate fractions


5x/10x^2+(-4x+3)/10x^2-4-3=0

We add all the numbers together, and all the variables

5x/10x^2+(-4x+3)/10x^2-7=0

We multiply all the terms by the denominator


5x+(-4x+3)-7*10x^2=0

Wy multiply elements

-70x^2+5x+(-4x+3)=0

We get rid of parentheses

-70x^2+5x-4x+3=0

We add all the numbers together, and all the variables

-70x^2+x+3=0

a = -70; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-70)·3
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*-70}=\frac{-30}{-140}
=3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*-70}=\frac{28}{-140}
=-1/5
$