3,5+11,5+25/100.x=x

Solution for 3,5+11,5+25/100.x=x equation:

3.5+11.5+25/100.x=x

We move all terms to the left:

3.5+11.5+25/100.x-(x)=0


Domain of the equation: 100.x!=0

x!=0/100.

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+25/100.x+15=0

We multiply all the terms by the denominator


-1x*100.x+15*100.x+25=0

Wy multiply elements

-100x^2+1500x+25=0

a = -100; b = 1500; c = +25;
Δ = b2-4ac
Δ = 15002-4·(-100)·25
Δ = 2260000
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:

$\sqrt{\Delta}=\sqrt{2260000}=\sqrt{10000*226}=\sqrt{10000}*\sqrt{226}=100\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1500)-100\sqrt{226}}{2*-100}=\frac{-1500-100\sqrt{226}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1500)+100\sqrt{226}}{2*-100}=\frac{-1500+100\sqrt{226}}{-200}
$