1/32x+10=1/4x+54

Solution for 1/32x+10=1/4x+54 equation:

1/32x+10=1/4x+54

We move all terms to the left:

1/32x+10-(1/4x+54)=0


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R



Domain of the equation: 4x+54)!=0

x∈R


We get rid of parentheses

1/32x-1/4x-54+10=0

We calculate fractions


4x/128x^2+(-32x)/128x^2-54+10=0

We add all the numbers together, and all the variables

4x/128x^2+(-32x)/128x^2-44=0

We multiply all the terms by the denominator


4x+(-32x)-44*128x^2=0

Wy multiply elements

-5632x^2+4x+(-32x)=0

We get rid of parentheses

-5632x^2+4x-32x=0

We add all the numbers together, and all the variables

-5632x^2-28x=0

a = -5632; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-5632)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*-5632}=\frac{0}{-11264}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-5632}=\frac{56}{-11264}
=-7/1408
$