1/32x=5x-6

Solution for 1/32x=5x-6 equation:

1/32x=5x-6

We move all terms to the left:

1/32x-(5x-6)=0


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R


We get rid of parentheses

1/32x-5x+6=0

We multiply all the terms by the denominator


-5x*32x+6*32x+1=0

Wy multiply elements

-160x^2+192x+1=0

a = -160; b = 192; c = +1;
Δ = b2-4ac
Δ = 1922-4·(-160)·1
Δ = 37504
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:

$\sqrt{\Delta}=\sqrt{37504}=\sqrt{64*586}=\sqrt{64}*\sqrt{586}=8\sqrt{586}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-8\sqrt{586}}{2*-160}=\frac{-192-8\sqrt{586}}{-320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+8\sqrt{586}}{2*-160}=\frac{-192+8\sqrt{586}}{-320}
$