7/4x+1/2x=7+9/2x

Solution for 7/4x+1/2x=7+9/2x equation:

7/4x+1/2x=7+9/2x

We move all terms to the left:

7/4x+1/2x-(7+9/2x)=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



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/4x+1/2x-(9/2x+7)=0

We get rid of parentheses

7/4x+1/2x-9/2x-7=0

We calculate fractions


14x/8x^2+(-36x+1)/8x^2-7=0

We multiply all the terms by the denominator


14x+(-36x+1)-7*8x^2=0

Wy multiply elements

-56x^2+14x+(-36x+1)=0

We get rid of parentheses

-56x^2+14x-36x+1=0

We add all the numbers together, and all the variables

-56x^2-22x+1=0

a = -56; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·(-56)·1
Δ = 708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{177}}{2*-56}=\frac{22-2\sqrt{177}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{177}}{2*-56}=\frac{22+2\sqrt{177}}{-112}
$