1/4x+4+1/2x+5=42

Solution for 1/4x+4+1/2x+5=42 equation:

1/4x+4+1/2x+5=42

We move all terms to the left:

1/4x+4+1/2x+5-(42)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x+1/2x-33=0

We calculate fractions


2x/8x^2+4x/8x^2-33=0

We multiply all the terms by the denominator


2x+4x-33*8x^2=0

We add all the numbers together, and all the variables

6x-33*8x^2=0

Wy multiply elements

-264x^2+6x=0

a = -264; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-264)·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*-264}=\frac{-12}{-528}
=1/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-264}=\frac{0}{-528}
=0
$