25/100x=65-x

Solution for 25/100x=65-x equation:

25/100x=65-x

We move all terms to the left:

25/100x-(65-x)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We add all the numbers together, and all the variables

25/100x-(-1x+65)=0

We get rid of parentheses

25/100x+1x-65=0

We multiply all the terms by the denominator


1x*100x-65*100x+25=0

Wy multiply elements

100x^2-6500x+25=0

a = 100; b = -6500; c = +25;
Δ = b2-4ac
Δ = -65002-4·100·25
Δ = 42240000
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:

$\sqrt{\Delta}=\sqrt{42240000}=\sqrt{640000*66}=\sqrt{640000}*\sqrt{66}=800\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6500)-800\sqrt{66}}{2*100}=\frac{6500-800\sqrt{66}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6500)+800\sqrt{66}}{2*100}=\frac{6500+800\sqrt{66}}{200}
$