3/5x+2=x+5

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

3/5x+2=x+5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2-25x+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 = 285
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{285}}{2*-5}=\frac{15-\sqrt{285}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{285}}{2*-5}=\frac{15+\sqrt{285}}{-10}
$