25/81x+15=x+20

Solution for 25/81x+15=x+20 equation:

25/81x+15=x+20

We move all terms to the left:

25/81x+15-(x+20)=0


Domain of the equation: 81x!=0

x!=0/81

x!=0

x∈R


We get rid of parentheses

25/81x-x-20+15=0

We multiply all the terms by the denominator


-x*81x-20*81x+15*81x+25=0

Wy multiply elements

-81x^2-1620x+1215x+25=0

We add all the numbers together, and all the variables

-81x^2-405x+25=0

a = -81; b = -405; c = +25;
Δ = b2-4ac
Δ = -4052-4·(-81)·25
Δ = 172125
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:

$\sqrt{\Delta}=\sqrt{172125}=\sqrt{2025*85}=\sqrt{2025}*\sqrt{85}=45\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-405)-45\sqrt{85}}{2*-81}=\frac{405-45\sqrt{85}}{-162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-405)+45\sqrt{85}}{2*-81}=\frac{405+45\sqrt{85}}{-162}
$