1/5x+x=28

Solution for 1/5x+x=28 equation:

1/5x+x=28

We move all terms to the left:

1/5x+x-(28)=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-28=0

We multiply all the terms by the denominator


x*5x-28*5x+1=0

Wy multiply elements

5x^2-140x+1=0

a = 5; b = -140; c = +1;
Δ = b2-4ac
Δ = -1402-4·5·1
Δ = 19580
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:

$\sqrt{\Delta}=\sqrt{19580}=\sqrt{4*4895}=\sqrt{4}*\sqrt{4895}=2\sqrt{4895}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4895}}{2*5}=\frac{140-2\sqrt{4895}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4895}}{2*5}=\frac{140+2\sqrt{4895}}{10}
$