1/5x+14x=20

Solution for 1/5x+14x=20 equation:

1/5x+14x=20

We move all terms to the left:

1/5x+14x-(20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

14x+1/5x-20=0

We multiply all the terms by the denominator


14x*5x-20*5x+1=0

Wy multiply elements

70x^2-100x+1=0

a = 70; b = -100; c = +1;
Δ = b2-4ac
Δ = -1002-4·70·1
Δ = 9720
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:

$\sqrt{\Delta}=\sqrt{9720}=\sqrt{324*30}=\sqrt{324}*\sqrt{30}=18\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-18\sqrt{30}}{2*70}=\frac{100-18\sqrt{30}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+18\sqrt{30}}{2*70}=\frac{100+18\sqrt{30}}{140}
$