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

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}
$