3/5x-2=3x-5

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

3/5x-2=3x-5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-15x^2+25x-10x+3=0

We add all the numbers together, and all the variables

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

a = -15; b = 15; c = +3;
Δ = b2-4ac
Δ = 152-4·(-15)·3
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9\sqrt{5}}{2*-15}=\frac{-15-9\sqrt{5}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9\sqrt{5}}{2*-15}=\frac{-15+9\sqrt{5}}{-30}
$