1/4x+3/4x+1/2x+2=5

Solution for 1/4x+3/4x+1/2x+2=5 equation:

1/4x+3/4x+1/2x+2=5

We move all terms to the left:

1/4x+3/4x+1/2x+2-(5)=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+3/4x+1/2x-3=0

We calculate fractions


(6x+1)/8x^2+4x/8x^2-3=0

We multiply all the terms by the denominator


(6x+1)+4x-3*8x^2=0

We add all the numbers together, and all the variables

4x+(6x+1)-3*8x^2=0

Wy multiply elements

-24x^2+4x+(6x+1)=0

We get rid of parentheses

-24x^2+4x+6x+1=0

We add all the numbers together, and all the variables

-24x^2+10x+1=0

a = -24; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-24)·1
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-24}=\frac{-24}{-48}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-24}=\frac{4}{-48}
=-1/12
$