X-5/x-3=7

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

X-5/X-3=7

We move all terms to the left:

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


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-5/X-10=0

We multiply all the terms by the denominator


X*X-10*X-5=0

We add all the numbers together, and all the variables

-10X+X*X-5=0

Wy multiply elements

X^2-10X-5=0

a = 1; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·1·(-5)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{30}}{2*1}=\frac{10-2\sqrt{30}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{30}}{2*1}=\frac{10+2\sqrt{30}}{2}
$