(-12/5)x=-2/3

Solution for (-12/5)x=-2/3 equation:

(-12/5)x=-2/3

We move all terms to the left:

(-12/5)x-(-2/3)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

-12x^2-(-2/3)=0

We get rid of parentheses

-12x^2+2/3=0

We multiply all the terms by the denominator


-12x^2*3+2=0

Wy multiply elements

-36x^2+2=0

a = -36; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-36)·2
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-36}=\frac{0-12\sqrt{2}}{-72}
=-\frac{12\sqrt{2}}{-72}
=-\frac{\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-36}=\frac{0+12\sqrt{2}}{-72}
=\frac{12\sqrt{2}}{-72}
=\frac{\sqrt{2}}{-6}
$