(-1/4)x=-2/3

Solution for (-1/4)x=-2/3 equation:

(-1/4)x=-2/3

We move all terms to the left:

(-1/4)x-(-2/3)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

-1x^2-(-2/3)=0

We get rid of parentheses

-1x^2+2/3=0

We multiply all the terms by the denominator


-1x^2*3+2=0

Wy multiply elements

-3x^2+2=0

a = -3; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-3)·2
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*-3}=\frac{0-2\sqrt{6}}{-6}
=-\frac{2\sqrt{6}}{-6}
=-\frac{\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*-3}=\frac{0+2\sqrt{6}}{-6}
=\frac{2\sqrt{6}}{-6}
=\frac{\sqrt{6}}{-3}
$