3/4w+1/2w-4=12

Solution for 3/4w+1/2w-4=12 equation:

3/4w+1/2w-4=12

We move all terms to the left:

3/4w+1/2w-4-(12)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

3/4w+1/2w-16=0

We calculate fractions


6w/8w^2+4w/8w^2-16=0

We multiply all the terms by the denominator


6w+4w-16*8w^2=0

We add all the numbers together, and all the variables

10w-16*8w^2=0

Wy multiply elements

-128w^2+10w=0

a = -128; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-128)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-128}=\frac{-20}{-256}
=5/64
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-128}=\frac{0}{-256}
=0
$