2x+25=2*1/5x+20

Solution for 2x+25=2*1/5x+20 equation:

2x+25=2*1/5x+20

We move all terms to the left:

2x+25-(2*1/5x+20)=0


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

x∈R


We get rid of parentheses

2x-2*1/5x-20+25=0

We multiply all the terms by the denominator


2x*5x-20*5x+25*5x-2*1=0

We add all the numbers together, and all the variables

2x*5x-20*5x+25*5x-2=0

Wy multiply elements

10x^2-100x+125x-2=0

We add all the numbers together, and all the variables

10x^2+25x-2=0

a = 10; b = 25; c = -2;
Δ = b2-4ac
Δ = 252-4·10·(-2)
Δ = 705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{705}}{2*10}=\frac{-25-\sqrt{705}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{705}}{2*10}=\frac{-25+\sqrt{705}}{20}
$