4/4x+7/x=7

Solution for 4/4x+7/x=7 equation:

4/4x+7/x=7

We move all terms to the left:

4/4x+7/x-(7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


4x/4x^2+28x/4x^2-7=0

We multiply all the terms by the denominator


4x+28x-7*4x^2=0

We add all the numbers together, and all the variables

32x-7*4x^2=0

Wy multiply elements

-28x^2+32x=0

a = -28; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-28)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-28}=\frac{-64}{-56}
=1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-28}=\frac{0}{-56}
=0
$