3/5x-2=-x+1

Solution for 3/5x-2=-x+1 equation:

3/5x-2=-x+1

We move all terms to the left:

3/5x-2-(-x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(-1x+1)-2=0

We get rid of parentheses

3/5x+1x-1-2=0

We multiply all the terms by the denominator


1x*5x-1*5x-2*5x+3=0

Wy multiply elements

5x^2-5x-10x+3=0

We add all the numbers together, and all the variables

5x^2-15x+3=0

a = 5; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·5·3
Δ = 165
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{165}}{2*5}=\frac{15-\sqrt{165}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{165}}{2*5}=\frac{15+\sqrt{165}}{10}
$