3/16x-25=x

Solution for 3/16x-25=x equation:

3/16x-25=x

We move all terms to the left:

3/16x-25-(x)=0


Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/16x-25=0

We multiply all the terms by the denominator


-1x*16x-25*16x+3=0

Wy multiply elements

-16x^2-400x+3=0

a = -16; b = -400; c = +3;
Δ = b2-4ac
Δ = -4002-4·(-16)·3
Δ = 160192
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:

$\sqrt{\Delta}=\sqrt{160192}=\sqrt{64*2503}=\sqrt{64}*\sqrt{2503}=8\sqrt{2503}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-8\sqrt{2503}}{2*-16}=\frac{400-8\sqrt{2503}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+8\sqrt{2503}}{2*-16}=\frac{400+8\sqrt{2503}}{-32}
$