3/5x+3=2x-4

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

3/5x+3=2x-4

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*5x+4*5x+3*5x+3=0

Wy multiply elements

-10x^2+20x+15x+3=0

We add all the numbers together, and all the variables

-10x^2+35x+3=0

a = -10; b = 35; c = +3;
Δ = b2-4ac
Δ = 352-4·(-10)·3
Δ = 1345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1345}}{2*-10}=\frac{-35-\sqrt{1345}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1345}}{2*-10}=\frac{-35+\sqrt{1345}}{-20}
$