3/5x+5=x-4

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

3/5x+5=x-4

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-5x^2+45x+3=0

a = -5; b = 45; c = +3;
Δ = b2-4ac
Δ = 452-4·(-5)·3
Δ = 2085
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{-(45)-\sqrt{2085}}{2*-5}=\frac{-45-\sqrt{2085}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2085}}{2*-5}=\frac{-45+\sqrt{2085}}{-10}
$