9/16x+280=x

Solution for 9/16x+280=x equation:

9/16x+280=x

We move all terms to the left:

9/16x+280-(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+9/16x+280=0

We multiply all the terms by the denominator


-1x*16x+280*16x+9=0

Wy multiply elements

-16x^2+4480x+9=0

a = -16; b = 4480; c = +9;
Δ = b2-4ac
Δ = 44802-4·(-16)·9
Δ = 20070976
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:

$\sqrt{\Delta}=\sqrt{20070976}=\sqrt{64*313609}=\sqrt{64}*\sqrt{313609}=8\sqrt{313609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4480)-8\sqrt{313609}}{2*-16}=\frac{-4480-8\sqrt{313609}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4480)+8\sqrt{313609}}{2*-16}=\frac{-4480+8\sqrt{313609}}{-32}
$