X-3/3x-5=1

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

X-3/3X-5=1

We move all terms to the left:

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


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-3/3X-6=0

We multiply all the terms by the denominator


X*3X-6*3X-3=0

Wy multiply elements

3X^2-18X-3=0

a = 3; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·3·(-3)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{10}}{2*3}=\frac{18-6\sqrt{10}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{10}}{2*3}=\frac{18+6\sqrt{10}}{6}
$