x/5x=2x+51

Solution for x/5x=2x+51 equation:

x/5x=2x+51

We move all terms to the left:

x/5x-(2x+51)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x/5x-2x-51=0

We multiply all the terms by the denominator


x-2x*5x-51*5x=0

Wy multiply elements

-10x^2+x-255x=0

We add all the numbers together, and all the variables

-10x^2-254x=0

a = -10; b = -254; c = 0;
Δ = b2-4ac
Δ = -2542-4·(-10)·0
Δ = 64516
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64516}=254$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-254)-254}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-254)+254}{2*-10}=\frac{508}{-20}
=-25+2/5
$