3/5x-2=2x+4

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

3/5x-2=2x+4

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-10x^2-30x+3=0

a = -10; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·(-10)·3
Δ = 1020
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{255}}{2*-10}=\frac{30-2\sqrt{255}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{255}}{2*-10}=\frac{30+2\sqrt{255}}{-20}
$