7/x=3/2x+22

Solution for 7/x=3/2x+22 equation:

7/x=3/2x+22

We move all terms to the left:

7/x-(3/2x+22)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+22)!=0

x∈R


We get rid of parentheses

7/x-3/2x-22=0

We calculate fractions


14x/2x^2+(-3x)/2x^2-22=0

We multiply all the terms by the denominator


14x+(-3x)-22*2x^2=0

Wy multiply elements

-44x^2+14x+(-3x)=0

We get rid of parentheses

-44x^2+14x-3x=0

We add all the numbers together, and all the variables

-44x^2+11x=0

a = -44; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-44)·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*-44}=\frac{-22}{-88}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-44}=\frac{0}{-88}
=0
$