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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x+2(-1x+3)-5=0

We multiply parentheses

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

We multiply all the terms by the denominator


-2x*3x+6*3x-5*3x+4=0

Wy multiply elements

-6x^2+18x-15x+4=0

We add all the numbers together, and all the variables

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

a = -6; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-6)·4
Δ = 105
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{-(3)-\sqrt{105}}{2*-6}=\frac{-3-\sqrt{105}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-6}=\frac{-3+\sqrt{105}}{-12}
$