X-5/x-3=7/1

Solution for X-5/x-3=7/1 equation:

X-5/X-3=7/1

We move all terms to the left:

X-5/X-3-(7/1)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-5/X-3-0=0

We add all the numbers together, and all the variables

X-5/X-3=0

We multiply all the terms by the denominator


X*X-3*X-5=0

We add all the numbers together, and all the variables

-3X+X*X-5=0

Wy multiply elements

X^2-3X-5=0

a = 1; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·1·(-5)
Δ = 29
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{29}}{2*1}=\frac{3-\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{29}}{2*1}=\frac{3+\sqrt{29}}{2}
$