4/3x-3=x-4

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



4/3x-3=x-4
We move all terms to the left:
4/3x-3-(x-4)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We get rid of parentheses
4/3x-x+4-3=0
We multiply all the terms by the denominator
-x*3x+4*3x-3*3x+4=0
Wy multiply elements
-3x^2+12x-9x+4=0
We add all the numbers together, and all the variables
-3x^2+3x+4=0
a = -3; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-3)·4
Δ = 57
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{57}}{2*-3}=\frac{-3-\sqrt{57}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-3}=\frac{-3+\sqrt{57}}{-6} $

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