10+1/2x+1/4x=54

Solution for 10+1/2x+1/4x=54 equation:

10+1/2x+1/4x=54

We move all terms to the left:

10+1/2x+1/4x-(54)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+1/4x-44=0

We calculate fractions


4x/8x^2+2x/8x^2-44=0

We multiply all the terms by the denominator


4x+2x-44*8x^2=0

We add all the numbers together, and all the variables

6x-44*8x^2=0

Wy multiply elements

-352x^2+6x=0

a = -352; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-352)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-352}=\frac{-12}{-704}
=3/176
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-352}=\frac{0}{-704}
=0
$