4/x+7=3/2x-4

Solution for 4/x+7=3/2x-4 equation:

4/x+7=3/2x-4

We move all terms to the left:

4/x+7-(3/2x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

4/x-3/2x+4+7=0

We calculate fractions


8x/2x^2+(-3x)/2x^2+4+7=0

We add all the numbers together, and all the variables

8x/2x^2+(-3x)/2x^2+11=0

We multiply all the terms by the denominator


8x+(-3x)+11*2x^2=0

Wy multiply elements

22x^2+8x+(-3x)=0

We get rid of parentheses

22x^2+8x-3x=0

We add all the numbers together, and all the variables

22x^2+5x=0

a = 22; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·22·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*22}=\frac{-10}{44}
=-5/22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*22}=\frac{0}{44}
=0
$