7(x+4)=2/3x+6

Solution for 7(x+4)=2/3x+6 equation:

7(x+4)=2/3x+6

We move all terms to the left:

7(x+4)-(2/3x+6)=0


Domain of the equation: 3x+6)!=0

x∈R


We multiply parentheses

7x-(2/3x+6)+28=0

We get rid of parentheses

7x-2/3x-6+28=0

We multiply all the terms by the denominator


7x*3x-6*3x+28*3x-2=0

Wy multiply elements

21x^2-18x+84x-2=0

We add all the numbers together, and all the variables

21x^2+66x-2=0

a = 21; b = 66; c = -2;
Δ = b2-4ac
Δ = 662-4·21·(-2)
Δ = 4524
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:

$\sqrt{\Delta}=\sqrt{4524}=\sqrt{4*1131}=\sqrt{4}*\sqrt{1131}=2\sqrt{1131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1131}}{2*21}=\frac{-66-2\sqrt{1131}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1131}}{2*21}=\frac{-66+2\sqrt{1131}}{42}
$