6-2/3x+5=4x

Solution for 6-2/3x+5=4x equation:

6-2/3x+5=4x

We move all terms to the left:

6-2/3x+5-(4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-2/3x+11=0

We multiply all the terms by the denominator


-4x*3x+11*3x-2=0

Wy multiply elements

-12x^2+33x-2=0

a = -12; b = 33; c = -2;
Δ = b2-4ac
Δ = 332-4·(-12)·(-2)
Δ = 993
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{993}}{2*-12}=\frac{-33-\sqrt{993}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{993}}{2*-12}=\frac{-33+\sqrt{993}}{-24}
$