7x-3/x-1=4

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

7x-3/x-1=4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7x-3/x-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

7x^2-5x-3=0

a = 7; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·7·(-3)
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*7}=\frac{5-\sqrt{109}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{109}}{2*7}=\frac{5+\sqrt{109}}{14}
$