(4/3)x-(1/3)=x+7

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Solution for (4/3)x-(1/3)=x+7 equation:



(4/3)x-(1/3)=x+7
We move all terms to the left:
(4/3)x-(1/3)-(x+7)=0
Domain of the equation: 3)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+4/3)x-(x+7)-(+1/3)=0
We multiply parentheses
4x^2-(x+7)-(+1/3)=0
We get rid of parentheses
4x^2-x-7-1/3=0
We multiply all the terms by the denominator
4x^2*3-x*3-1-7*3=0
We add all the numbers together, and all the variables
4x^2*3-x*3-22=0
Wy multiply elements
12x^2-3x-22=0
a = 12; b = -3; c = -22;
Δ = b2-4ac
Δ = -32-4·12·(-22)
Δ = 1065
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{1065}}{2*12}=\frac{3-\sqrt{1065}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1065}}{2*12}=\frac{3+\sqrt{1065}}{24} $

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