2x+(-3/5x+5)=(-8)

Solution for 2x+(-3/5x+5)=(-8) equation:

2x+(-3/5x+5)=(-8)

We move all terms to the left:

2x+(-3/5x+5)-((-8))=0


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

x∈R


We add all the numbers together, and all the variables

2x+(-3/5x+5)+8=0

We get rid of parentheses

2x-3/5x+5+8=0

We multiply all the terms by the denominator


2x*5x+5*5x+8*5x-3=0

Wy multiply elements

10x^2+25x+40x-3=0

We add all the numbers together, and all the variables

10x^2+65x-3=0

a = 10; b = 65; c = -3;
Δ = b2-4ac
Δ = 652-4·10·(-3)
Δ = 4345
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{-(65)-\sqrt{4345}}{2*10}=\frac{-65-\sqrt{4345}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4345}}{2*10}=\frac{-65+\sqrt{4345}}{20}
$