X+1/16x-75=0

Solution for X+1/16x-75=0 equation:

X+1/16X-75=0


Domain of the equation: 16X!=0

X!=0/16

X!=0

X∈R


We multiply all the terms by the denominator


X*16X-75*16X+1=0

Wy multiply elements

16X^2-1200X+1=0

a = 16; b = -1200; c = +1;
Δ = b2-4ac
Δ = -12002-4·16·1
Δ = 1439936
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:

$\sqrt{\Delta}=\sqrt{1439936}=\sqrt{64*22499}=\sqrt{64}*\sqrt{22499}=8\sqrt{22499}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-8\sqrt{22499}}{2*16}=\frac{1200-8\sqrt{22499}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+8\sqrt{22499}}{2*16}=\frac{1200+8\sqrt{22499}}{32}
$