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

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

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

We move all terms to the left:

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


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

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

We get rid of parentheses

-1x^2+3/4=0

We multiply all the terms by the denominator


-1x^2*4+3=0

Wy multiply elements

-4x^2+3=0

a = -4; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-4)·3
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-4}=\frac{0-4\sqrt{3}}{-8}
=-\frac{4\sqrt{3}}{-8}
=-\frac{\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-4}=\frac{0+4\sqrt{3}}{-8}
=\frac{4\sqrt{3}}{-8}
=\frac{\sqrt{3}}{-2}
$