2x+3=1/5x-5

Solution for 2x+3=1/5x-5 equation:

2x+3=1/5x-5

We move all terms to the left:

2x+3-(1/5x-5)=0


Domain of the equation: 5x-5)!=0

x∈R


We get rid of parentheses

2x-1/5x+5+3=0

We multiply all the terms by the denominator


2x*5x+5*5x+3*5x-1=0

Wy multiply elements

10x^2+25x+15x-1=0

We add all the numbers together, and all the variables

10x^2+40x-1=0

a = 10; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·10·(-1)
Δ = 1640
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:

$\sqrt{\Delta}=\sqrt{1640}=\sqrt{4*410}=\sqrt{4}*\sqrt{410}=2\sqrt{410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{410}}{2*10}=\frac{-40-2\sqrt{410}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{410}}{2*10}=\frac{-40+2\sqrt{410}}{20}
$