3/5x=x+20

Solution for 3/5x=x+20 equation:

3/5x=x+20

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-x-20=0

We multiply all the terms by the denominator


-x*5x-20*5x+3=0

Wy multiply elements

-5x^2-100x+3=0

a = -5; b = -100; c = +3;
Δ = b2-4ac
Δ = -1002-4·(-5)·3
Δ = 10060
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:

$\sqrt{\Delta}=\sqrt{10060}=\sqrt{4*2515}=\sqrt{4}*\sqrt{2515}=2\sqrt{2515}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2515}}{2*-5}=\frac{100-2\sqrt{2515}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2515}}{2*-5}=\frac{100+2\sqrt{2515}}{-10}
$