1/32x=42x-5

Solution for 1/32x=42x-5 equation:

1/32x=42x-5

We move all terms to the left:

1/32x-(42x-5)=0


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R


We get rid of parentheses

1/32x-42x+5=0

We multiply all the terms by the denominator


-42x*32x+5*32x+1=0

Wy multiply elements

-1344x^2+160x+1=0

a = -1344; b = 160; c = +1;
Δ = b2-4ac
Δ = 1602-4·(-1344)·1
Δ = 30976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30976}=176$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-176}{2*-1344}=\frac{-336}{-2688}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+176}{2*-1344}=\frac{16}{-2688}
=-1/168
$