3/5x-2=2x-7

Solution for 3/5x-2=2x-7 equation:

3/5x-2=2x-7

We move all terms to the left:

3/5x-2-(2x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-2x+7-2=0

We multiply all the terms by the denominator


-2x*5x+7*5x-2*5x+3=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -10; b = 25; c = +3;
Δ = b2-4ac
Δ = 252-4·(-10)·3
Δ = 745
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{-(25)-\sqrt{745}}{2*-10}=\frac{-25-\sqrt{745}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{745}}{2*-10}=\frac{-25+\sqrt{745}}{-20}
$