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

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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!=0

x!=0/5

x!=0

x∈R



We add all the numbers together, and all the variables

2x+3/5x+13=0

We multiply all the terms by the denominator


2x*5x+13*5x+3=0

Wy multiply elements

10x^2+65x+3=0

a = 10; b = 65; c = +3;
Δ = b2-4ac
Δ = 652-4·10·3
Δ = 4105
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{4105}}{2*10}=\frac{-65-\sqrt{4105}}{20}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4105}}{2*10}=\frac{-65+\sqrt{4105}}{20}
$

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