4/3x-1=x+7

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

4/3x-1=x+7

We move all terms to the left:

4/3x-1-(x+7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-x-7-1=0

We multiply all the terms by the denominator


-x*3x-7*3x-1*3x+4=0

Wy multiply elements

-3x^2-21x-3x+4=0

We add all the numbers together, and all the variables

-3x^2-24x+4=0

a = -3; b = -24; c = +4;
Δ = b2-4ac
Δ = -242-4·(-3)·4
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*-3}=\frac{24-4\sqrt{39}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*-3}=\frac{24+4\sqrt{39}}{-6}
$