4/3(x)=x+7

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

4/3(x)=x+7

We move all terms to the left:

4/3(x)-(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=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -3; b = -21; c = +4;
Δ = b2-4ac
Δ = -212-4·(-3)·4
Δ = 489
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{-(-21)-\sqrt{489}}{2*-3}=\frac{21-\sqrt{489}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{489}}{2*-3}=\frac{21+\sqrt{489}}{-6}
$