17/2x+120=16x

Solution for 17/2x+120=16x equation:

17/2x+120=16x

We move all terms to the left:

17/2x+120-(16x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-16x+17/2x+120=0

We multiply all the terms by the denominator


-16x*2x+120*2x+17=0

Wy multiply elements

-32x^2+240x+17=0

a = -32; b = 240; c = +17;
Δ = b2-4ac
Δ = 2402-4·(-32)·17
Δ = 59776
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:

$\sqrt{\Delta}=\sqrt{59776}=\sqrt{64*934}=\sqrt{64}*\sqrt{934}=8\sqrt{934}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-8\sqrt{934}}{2*-32}=\frac{-240-8\sqrt{934}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+8\sqrt{934}}{2*-32}=\frac{-240+8\sqrt{934}}{-64}
$