5/2x+1/4x+1=12

Solution for 5/2x+1/4x+1=12 equation:

5/2x+1/4x+1=12

We move all terms to the left:

5/2x+1/4x+1-(12)=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

5/2x+1/4x-11=0

We calculate fractions


20x/8x^2+2x/8x^2-11=0

We multiply all the terms by the denominator


20x+2x-11*8x^2=0

We add all the numbers together, and all the variables

22x-11*8x^2=0

Wy multiply elements

-88x^2+22x=0

a = -88; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-88)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-88}=\frac{-44}{-176}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-88}=\frac{0}{-176}
=0
$