3x-4=1/25x+20

Solution for 3x-4=1/25x+20 equation:

3x-4=1/25x+20

We move all terms to the left:

3x-4-(1/25x+20)=0


Domain of the equation: 25x+20)!=0

x∈R


We get rid of parentheses

3x-1/25x-20-4=0

We multiply all the terms by the denominator


3x*25x-20*25x-4*25x-1=0

Wy multiply elements

75x^2-500x-100x-1=0

We add all the numbers together, and all the variables

75x^2-600x-1=0

a = 75; b = -600; c = -1;
Δ = b2-4ac
Δ = -6002-4·75·(-1)
Δ = 360300
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:

$\sqrt{\Delta}=\sqrt{360300}=\sqrt{100*3603}=\sqrt{100}*\sqrt{3603}=10\sqrt{3603}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-10\sqrt{3603}}{2*75}=\frac{600-10\sqrt{3603}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+10\sqrt{3603}}{2*75}=\frac{600+10\sqrt{3603}}{150}
$