2x-4=3/5x+3

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

2x-4=3/5x+3

We move all terms to the left:

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


Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-15x-20x-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}
$