X-2/3x=14

Solution for X-2/3x=14 equation:

X-2/3X=14

We move all terms to the left:

X-2/3X-(14)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-14*3X-2=0

Wy multiply elements

3X^2-42X-2=0

a = 3; b = -42; c = -2;
Δ = b2-4ac
Δ = -422-4·3·(-2)
Δ = 1788
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:

$\sqrt{\Delta}=\sqrt{1788}=\sqrt{4*447}=\sqrt{4}*\sqrt{447}=2\sqrt{447}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{447}}{2*3}=\frac{42-2\sqrt{447}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{447}}{2*3}=\frac{42+2\sqrt{447}}{6}
$