4/3x=6x-14

Solution for 4/3x=6x-14 equation:

4/3x=6x-14

We move all terms to the left:

4/3x-(6x-14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-6x+14=0

We multiply all the terms by the denominator


-6x*3x+14*3x+4=0

Wy multiply elements

-18x^2+42x+4=0

a = -18; b = 42; c = +4;
Δ = b2-4ac
Δ = 422-4·(-18)·4
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{57}}{2*-18}=\frac{-42-6\sqrt{57}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{57}}{2*-18}=\frac{-42+6\sqrt{57}}{-36}
$