3/5x-5+x-4=-1x

Solution for 3/5x-5+x-4=-1x equation:

3/5x-5+x-4=-1x

We move all terms to the left:

3/5x-5+x-4-(-1x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/5x-(-1x)-9=0

We get rid of parentheses

x+3/5x+1x-9=0

We multiply all the terms by the denominator


x*5x+1x*5x-9*5x+3=0

Wy multiply elements

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

We add all the numbers together, and all the variables

10x^2-45x+3=0

a = 10; b = -45; c = +3;
Δ = b2-4ac
Δ = -452-4·10·3
Δ = 1905
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{1905}}{2*10}=\frac{45-\sqrt{1905}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1905}}{2*10}=\frac{45+\sqrt{1905}}{20}
$