2x+3=4/5x

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

2x+3=4/5x

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-4/5x+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2+15x-4=0

a = 10; b = 15; c = -4;
Δ = b2-4ac
Δ = 152-4·10·(-4)
Δ = 385
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{-(15)-\sqrt{385}}{2*10}=\frac{-15-\sqrt{385}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{385}}{2*10}=\frac{-15+\sqrt{385}}{20}
$