3/5x+4=x+5

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

3/5x+4=x+5

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2-25x+20x+3=0

We add all the numbers together, and all the variables

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

a = -5; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-5)·3
Δ = 85
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{-(-5)-\sqrt{85}}{2*-5}=\frac{5-\sqrt{85}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{85}}{2*-5}=\frac{5+\sqrt{85}}{-10}
$