(6/11)x=36/5

Solution for (6/11)x=36/5 equation:

(6/11)x=36/5

We move all terms to the left:

(6/11)x-(36/5)=0


Domain of the equation: 11)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+6/11)x-(+36/5)=0

We multiply parentheses

6x^2-(+36/5)=0

We get rid of parentheses

6x^2-36/5=0

We multiply all the terms by the denominator


6x^2*5-36=0

Wy multiply elements

30x^2-36=0

a = 30; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·30·(-36)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{30}}{2*30}=\frac{0-12\sqrt{30}}{60}
=-\frac{12\sqrt{30}}{60}
=-\frac{\sqrt{30}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{30}}{2*30}=\frac{0+12\sqrt{30}}{60}
=\frac{12\sqrt{30}}{60}
=\frac{\sqrt{30}}{5}
$