2/x+2+6/5x+10=7

Solution for 2/x+2+6/5x+10=7 equation:

2/x+2+6/5x+10=7

We move all terms to the left:

2/x+2+6/5x+10-(7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+6/5x+5=0

We calculate fractions


10x/5x^2+6x/5x^2+5=0

We multiply all the terms by the denominator


10x+6x+5*5x^2=0

We add all the numbers together, and all the variables

16x+5*5x^2=0

Wy multiply elements

25x^2+16x=0

a = 25; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·25·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*25}=\frac{-32}{50}
=-16/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*25}=\frac{0}{50}
=0
$