1/2g+1+3/4g=-9

Solution for 1/2g+1+3/4g=-9 equation:

1/2g+1+3/4g=-9

We move all terms to the left:

1/2g+1+3/4g-(-9)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R



Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R


We add all the numbers together, and all the variables

1/2g+3/4g+10=0

We calculate fractions


4g/8g^2+6g/8g^2+10=0

We multiply all the terms by the denominator


4g+6g+10*8g^2=0

We add all the numbers together, and all the variables

10g+10*8g^2=0

Wy multiply elements

80g^2+10g=0

a = 80; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·80·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*80}=\frac{-20}{160}
=-1/8
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*80}=\frac{0}{160}
=0
$