17/32x+320=X

Solution for 17/32x+320=X equation:

17/32x+320=x

We move all terms to the left:

17/32x+320-(x)=0


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+17/32x+320=0

We multiply all the terms by the denominator


-1x*32x+320*32x+17=0

Wy multiply elements

-32x^2+10240x+17=0

a = -32; b = 10240; c = +17;
Δ = b2-4ac
Δ = 102402-4·(-32)·17
Δ = 104859776
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:

$\sqrt{\Delta}=\sqrt{104859776}=\sqrt{64*1638434}=\sqrt{64}*\sqrt{1638434}=8\sqrt{1638434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10240)-8\sqrt{1638434}}{2*-32}=\frac{-10240-8\sqrt{1638434}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10240)+8\sqrt{1638434}}{2*-32}=\frac{-10240+8\sqrt{1638434}}{-64}
$