1x+2/5x=-5

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

1x+2/5x=-5

We move all terms to the left:

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

We multiply all the terms by the denominator


x*5x+5*5x+2=0

Wy multiply elements

5x^2+25x+2=0

a = 5; b = 25; c = +2;
Δ = b2-4ac
Δ = 252-4·5·2
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-3\sqrt{65}}{2*5}=\frac{-25-3\sqrt{65}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+3\sqrt{65}}{2*5}=\frac{-25+3\sqrt{65}}{10}
$