2/5x+103/5x=2x+5

Solution for 2/5x+103/5x=2x+5 equation:

2/5x+103/5x=2x+5

We move all terms to the left:

2/5x+103/5x-(2x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x+103/5x-2x-5=0

We multiply all the terms by the denominator


-2x*5x-5*5x+2+103=0

We add all the numbers together, and all the variables

-2x*5x-5*5x+105=0

Wy multiply elements

-10x^2-25x+105=0

a = -10; b = -25; c = +105;
Δ = b2-4ac
Δ = -252-4·(-10)·105
Δ = 4825
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:

$\sqrt{\Delta}=\sqrt{4825}=\sqrt{25*193}=\sqrt{25}*\sqrt{193}=5\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{193}}{2*-10}=\frac{25-5\sqrt{193}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{193}}{2*-10}=\frac{25+5\sqrt{193}}{-20}
$