1/5x+5x=18-7x

Solution for 1/5x+5x=18-7x equation:

1/5x+5x=18-7x

We move all terms to the left:

1/5x+5x-(18-7x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x+5x-(-7x+18)=0

We add all the numbers together, and all the variables

5x+1/5x-(-7x+18)=0

We get rid of parentheses

5x+1/5x+7x-18=0

We multiply all the terms by the denominator


5x*5x+7x*5x-18*5x+1=0

Wy multiply elements

25x^2+35x^2-90x+1=0

We add all the numbers together, and all the variables

60x^2-90x+1=0

a = 60; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·60·1
Δ = 7860
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:

$\sqrt{\Delta}=\sqrt{7860}=\sqrt{4*1965}=\sqrt{4}*\sqrt{1965}=2\sqrt{1965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1965}}{2*60}=\frac{90-2\sqrt{1965}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1965}}{2*60}=\frac{90+2\sqrt{1965}}{120}
$