11/6x=3x-14

Solution for 11/6x=3x-14 equation:

11/6x=3x-14

We move all terms to the left:

11/6x-(3x-14)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

11/6x-3x+14=0

We multiply all the terms by the denominator


-3x*6x+14*6x+11=0

Wy multiply elements

-18x^2+84x+11=0

a = -18; b = 84; c = +11;
Δ = b2-4ac
Δ = 842-4·(-18)·11
Δ = 7848
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:

$\sqrt{\Delta}=\sqrt{7848}=\sqrt{36*218}=\sqrt{36}*\sqrt{218}=6\sqrt{218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-6\sqrt{218}}{2*-18}=\frac{-84-6\sqrt{218}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+6\sqrt{218}}{2*-18}=\frac{-84+6\sqrt{218}}{-36}
$