(12/5)x=118/15

Solution for (12/5)x=118/15 equation:

(12/5)x=118/15

We move all terms to the left:

(12/5)x-(118/15)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+12/5)x-(+118/15)=0

We multiply parentheses

12x^2-(+118/15)=0

We get rid of parentheses

12x^2-118/15=0

We multiply all the terms by the denominator


12x^2*15-118=0

Wy multiply elements

180x^2-118=0

a = 180; b = 0; c = -118;
Δ = b2-4ac
Δ = 02-4·180·(-118)
Δ = 84960
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:

$\sqrt{\Delta}=\sqrt{84960}=\sqrt{144*590}=\sqrt{144}*\sqrt{590}=12\sqrt{590}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{590}}{2*180}=\frac{0-12\sqrt{590}}{360}
=-\frac{12\sqrt{590}}{360}
=-\frac{\sqrt{590}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{590}}{2*180}=\frac{0+12\sqrt{590}}{360}
=\frac{12\sqrt{590}}{360}
=\frac{\sqrt{590}}{30}
$