2/5x+10+3/5x=2x+5

Solution for 2/5x+10+3/5x=2x+5 equation:

2/5x+10+3/5x=2x+5

We move all terms to the left:

2/5x+10+3/5x-(2x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x+3/5x-2x-5+10=0

We multiply all the terms by the denominator


-2x*5x-5*5x+10*5x+2+3=0

We add all the numbers together, and all the variables

-2x*5x-5*5x+10*5x+5=0

Wy multiply elements

-10x^2-25x+50x+5=0

We add all the numbers together, and all the variables

-10x^2+25x+5=0

a = -10; b = 25; c = +5;
Δ = b2-4ac
Δ = 252-4·(-10)·5
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{33}}{2*-10}=\frac{-25-5\sqrt{33}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{33}}{2*-10}=\frac{-25+5\sqrt{33}}{-20}
$