3/4*w=12

Solution for 3/4*w=12 equation:

3/4*w=12

We move all terms to the left:

3/4*w-(12)=0


Domain of the equation: 4*w!=0

w!=0/1

w!=0

w∈R


We multiply all the terms by the denominator


-12*4*w+3=0

Wy multiply elements

-48w*w+3=0

Wy multiply elements

-48w^2+3=0

a = -48; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-48)·3
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-48}=\frac{-24}{-96}
=1/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-48}=\frac{24}{-96}
=-1/4
$