4x+3/x+7=3x+4/x+4

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

4x+3/x+7=3x+4/x+4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


4x*x-3x*x-4*x+7*x+3-4=0

We add all the numbers together, and all the variables

3x+4x*x-3x*x-1=0

Wy multiply elements

4x^2-3x^2+3x-1=0

We add all the numbers together, and all the variables

x^2+3x-1=0

a = 1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·1·(-1)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{13}}{2*1}=\frac{-3-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{13}}{2*1}=\frac{-3+\sqrt{13}}{2}
$