1/7x+1/4x=22

Solution for 1/7x+1/4x=22 equation:

1/7x+1/4x=22

We move all terms to the left:

1/7x+1/4x-(22)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


4x/28x^2+7x/28x^2-22=0

We multiply all the terms by the denominator


4x+7x-22*28x^2=0

We add all the numbers together, and all the variables

11x-22*28x^2=0

Wy multiply elements

-616x^2+11x=0

a = -616; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-616)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-616}=\frac{-22}{-1232}
=1/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-616}=\frac{0}{-1232}
=0
$