(5/9)x=8/12

Solution for (5/9)x=8/12 equation:

(5/9)x=8/12

We move all terms to the left:

(5/9)x-(8/12)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/9)x-(+8/12)=0

We multiply parentheses

5x^2-(+8/12)=0

We get rid of parentheses

5x^2-8/12=0

We multiply all the terms by the denominator


5x^2*12-8=0

Wy multiply elements

60x^2-8=0

a = 60; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·60·(-8)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*60}=\frac{0-8\sqrt{30}}{120}
=-\frac{8\sqrt{30}}{120}
=-\frac{\sqrt{30}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*60}=\frac{0+8\sqrt{30}}{120}
=\frac{8\sqrt{30}}{120}
=\frac{\sqrt{30}}{15}
$