5-2/8g=1/2g-4

Solution for 5-2/8g=1/2g-4 equation:

5-2/8g=1/2g-4

We move all terms to the left:

5-2/8g-(1/2g-4)=0


Domain of the equation: 8g!=0

g!=0/8

g!=0

g∈R



Domain of the equation: 2g-4)!=0

g∈R


We get rid of parentheses

-2/8g-1/2g+4+5=0

We calculate fractions


(-4g)/16g^2+(-8g)/16g^2+4+5=0

We add all the numbers together, and all the variables

(-4g)/16g^2+(-8g)/16g^2+9=0

We multiply all the terms by the denominator


(-4g)+(-8g)+9*16g^2=0

Wy multiply elements

144g^2+(-4g)+(-8g)=0

We get rid of parentheses

144g^2-4g-8g=0

We add all the numbers together, and all the variables

144g^2-12g=0

a = 144; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·144·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*144}=\frac{0}{288}
=0
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*144}=\frac{24}{288}
=1/12
$