(2/3)(x+13)=22

Solution for (2/3)(x+13)=22 equation:

(2/3)(x+13)=22

We move all terms to the left:

(2/3)(x+13)-(22)=0


Domain of the equation: 3)(x+13)!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)(x+13)-22=0

We multiply parentheses ..

(+2x^2+2/3*13)-22=0

We multiply all the terms by the denominator


(+2x^2+2-22*3*13)=0

We get rid of parentheses

2x^2+2-22*3*13=0

We add all the numbers together, and all the variables

2x^2-856=0

a = 2; b = 0; c = -856;
Δ = b2-4ac
Δ = 02-4·2·(-856)
Δ = 6848
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:

$\sqrt{\Delta}=\sqrt{6848}=\sqrt{64*107}=\sqrt{64}*\sqrt{107}=8\sqrt{107}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{107}}{2*2}=\frac{0-8\sqrt{107}}{4}
=-\frac{8\sqrt{107}}{4}
=-2\sqrt{107}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{107}}{2*2}=\frac{0+8\sqrt{107}}{4}
=\frac{8\sqrt{107}}{4}
=2\sqrt{107}
$