35/100(x)+39=x

Solution for 35/100(x)+39=x equation:

35/100(x)+39=x

We move all terms to the left:

35/100(x)+39-(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

-1x+35/100x+39=0

We multiply all the terms by the denominator


-1x*100x+39*100x+35=0

Wy multiply elements

-100x^2+3900x+35=0

a = -100; b = 3900; c = +35;
Δ = b2-4ac
Δ = 39002-4·(-100)·35
Δ = 15224000
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:

$\sqrt{\Delta}=\sqrt{15224000}=\sqrt{1600*9515}=\sqrt{1600}*\sqrt{9515}=40\sqrt{9515}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3900)-40\sqrt{9515}}{2*-100}=\frac{-3900-40\sqrt{9515}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3900)+40\sqrt{9515}}{2*-100}=\frac{-3900+40\sqrt{9515}}{-200}
$