(5/6)x=300/432

Solution for (5/6)x=300/432 equation:

(5/6)x=300/432

We move all terms to the left:

(5/6)x-(300/432)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/6)x-(+300/432)=0

We multiply parentheses

5x^2-(+300/432)=0

We get rid of parentheses

5x^2-300/432=0

We multiply all the terms by the denominator


5x^2*432-300=0

Wy multiply elements

2160x^2-300=0

a = 2160; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·2160·(-300)
Δ = 2592000
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:

$\sqrt{\Delta}=\sqrt{2592000}=\sqrt{518400*5}=\sqrt{518400}*\sqrt{5}=720\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-720\sqrt{5}}{2*2160}=\frac{0-720\sqrt{5}}{4320}
=-\frac{720\sqrt{5}}{4320}
=-\frac{\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+720\sqrt{5}}{2*2160}=\frac{0+720\sqrt{5}}{4320}
=\frac{720\sqrt{5}}{4320}
=\frac{\sqrt{5}}{6}
$