3x-50=1/5x+20

Solution for 3x-50=1/5x+20 equation:

3x-50=1/5x+20

We move all terms to the left:

3x-50-(1/5x+20)=0


Domain of the equation: 5x+20)!=0

x∈R


We get rid of parentheses

3x-1/5x-20-50=0

We multiply all the terms by the denominator


3x*5x-20*5x-50*5x-1=0

Wy multiply elements

15x^2-100x-250x-1=0

We add all the numbers together, and all the variables

15x^2-350x-1=0

a = 15; b = -350; c = -1;
Δ = b2-4ac
Δ = -3502-4·15·(-1)
Δ = 122560
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:

$\sqrt{\Delta}=\sqrt{122560}=\sqrt{64*1915}=\sqrt{64}*\sqrt{1915}=8\sqrt{1915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-8\sqrt{1915}}{2*15}=\frac{350-8\sqrt{1915}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+8\sqrt{1915}}{2*15}=\frac{350+8\sqrt{1915}}{30}
$