(2/3)*(x+4)=14

Solution for (2/3)*(x+4)=14 equation:

(2/3)(x+4)=14

We move all terms to the left:

(2/3)(x+4)-(14)=0


Domain of the equation: 3)(x+4)!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)(x+4)-14=0

We multiply parentheses ..

(+2x^2+2/3*4)-14=0

We multiply all the terms by the denominator


(+2x^2+2-14*3*4)=0

We get rid of parentheses

2x^2+2-14*3*4=0

We add all the numbers together, and all the variables

2x^2-166=0

a = 2; b = 0; c = -166;
Δ = b2-4ac
Δ = 02-4·2·(-166)
Δ = 1328
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:

$\sqrt{\Delta}=\sqrt{1328}=\sqrt{16*83}=\sqrt{16}*\sqrt{83}=4\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{83}}{2*2}=\frac{0-4\sqrt{83}}{4}
=-\frac{4\sqrt{83}}{4}
=-\sqrt{83}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{83}}{2*2}=\frac{0+4\sqrt{83}}{4}
=\frac{4\sqrt{83}}{4}
=\sqrt{83}
$