1/5x+x=7

Solution for 1/5x+x=7 equation:

1/5x+x=7

We move all terms to the left:

1/5x+x-(7)=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+1/5x-7=0

We multiply all the terms by the denominator


x*5x-7*5x+1=0

Wy multiply elements

5x^2-35x+1=0

a = 5; b = -35; c = +1;
Δ = b2-4ac
Δ = -352-4·5·1
Δ = 1205
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{-(-35)-\sqrt{1205}}{2*5}=\frac{35-\sqrt{1205}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1205}}{2*5}=\frac{35+\sqrt{1205}}{10}
$