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

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

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

We move all terms to the left:

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

x+3/5x-10=0

We multiply all the terms by the denominator


x*5x-10*5x+3=0

Wy multiply elements

5x^2-50x+3=0

a = 5; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·5·3
Δ = 2440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2440}=\sqrt{4*610}=\sqrt{4}*\sqrt{610}=2\sqrt{610}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{610}}{2*5}=\frac{50-2\sqrt{610}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{610}}{2*5}=\frac{50+2\sqrt{610}}{10}
$