4/3x+3-x=1

Solution for 4/3x+3-x=1 equation:

4/3x+3-x=1

We move all terms to the left:

4/3x+3-x-(1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/3x+2=0

We multiply all the terms by the denominator


-1x*3x+2*3x+4=0

Wy multiply elements

-3x^2+6x+4=0

a = -3; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-3)·4
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*-3}=\frac{-6-2\sqrt{21}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-3}=\frac{-6+2\sqrt{21}}{-6}
$