X-4/x*3=1

Solution for X-4/x*3=1 equation:

X-4/X*3=1

We move all terms to the left:

X-4/X*3-(1)=0


Domain of the equation: X*3!=0

X!=0/1

X!=0

X∈R


We multiply all the terms by the denominator


X*X*3-1*X*3-4=0

Wy multiply elements

3X^2*3-3X*3-4=0

Wy multiply elements

9X^2-9X-4=0

a = 9; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·9·(-4)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*9}=\frac{-6}{18}
=-1/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*9}=\frac{24}{18}
=1+1/3
$