3/4g-1/2g+4=20

Solution for 3/4g-1/2g+4=20 equation:

3/4g-1/2g+4=20

We move all terms to the left:

3/4g-1/2g+4-(20)=0


Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R



Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R


We add all the numbers together, and all the variables

3/4g-1/2g-16=0

We calculate fractions


6g/8g^2+(-4g)/8g^2-16=0

We multiply all the terms by the denominator


6g+(-4g)-16*8g^2=0

Wy multiply elements

-128g^2+6g+(-4g)=0

We get rid of parentheses

-128g^2+6g-4g=0

We add all the numbers together, and all the variables

-128g^2+2g=0

a = -128; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-128)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-128}=\frac{-4}{-256}
=1/64
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-128}=\frac{0}{-256}
=0
$