x/5x+14+2x+2=30

Solution for x/5x+14+2x+2=30 equation:

x/5x+14+2x+2=30

We move all terms to the left:

x/5x+14+2x+2-(30)=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+x/5x-14=0

We multiply all the terms by the denominator


2x*5x+x-14*5x=0

We add all the numbers together, and all the variables

x+2x*5x-14*5x=0

Wy multiply elements

10x^2+x-70x=0

We add all the numbers together, and all the variables

10x^2-69x=0

a = 10; b = -69; c = 0;
Δ = b2-4ac
Δ = -692-4·10·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-69}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+69}{2*10}=\frac{138}{20}
=6+9/10
$