7/2x+5=4/x-3

Solution for 7/2x+5=4/x-3 equation:

7/2x+5=4/x-3

We move all terms to the left:

7/2x+5-(4/x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

7/2x-4/x+3+5=0

We calculate fractions


7x/2x^2+(-8x)/2x^2+3+5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2+7x+(-8x)=0

We get rid of parentheses

16x^2+7x-8x=0

We add all the numbers together, and all the variables

16x^2-1x=0

a = 16; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·16·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*16}=\frac{2}{32}
=1/16
$