(4/9)(x+13)=8

Solution for (4/9)(x+13)=8 equation:

(4/9)(x+13)=8

We move all terms to the left:

(4/9)(x+13)-(8)=0


Domain of the equation: 9)(x+13)!=0

x∈R


We add all the numbers together, and all the variables

(+4/9)(x+13)-8=0

We multiply parentheses ..

(+4x^2+4/9*13)-8=0

We multiply all the terms by the denominator


(+4x^2+4-8*9*13)=0

We get rid of parentheses

4x^2+4-8*9*13=0

We add all the numbers together, and all the variables

4x^2-932=0

a = 4; b = 0; c = -932;
Δ = b2-4ac
Δ = 02-4·4·(-932)
Δ = 14912
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:

$\sqrt{\Delta}=\sqrt{14912}=\sqrt{64*233}=\sqrt{64}*\sqrt{233}=8\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{233}}{2*4}=\frac{0-8\sqrt{233}}{8}
=-\frac{8\sqrt{233}}{8}
=-\sqrt{233}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{233}}{2*4}=\frac{0+8\sqrt{233}}{8}
=\frac{8\sqrt{233}}{8}
=\sqrt{233}
$