3x-1=7/x+4

Solution for 3x-1=7/x+4 equation:

3x-1=7/x+4

We move all terms to the left:

3x-1-(7/x+4)=0


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

x∈R


We get rid of parentheses

3x-7/x-4-1=0

We multiply all the terms by the denominator


3x*x-4*x-1*x-7=0

We add all the numbers together, and all the variables

-5x+3x*x-7=0

Wy multiply elements

3x^2-5x-7=0

a = 3; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·3·(-7)
Δ = 109
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{-(-5)-\sqrt{109}}{2*3}=\frac{5-\sqrt{109}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{109}}{2*3}=\frac{5+\sqrt{109}}{6}
$