-g+6+(1/2)g-9=71/2

Solution for -g+6+(1/2)g-9=71/2 equation:

-g+6+(1/2)g-9=71/2

We move all terms to the left:

-g+6+(1/2)g-9-(71/2)=0


Domain of the equation: 2)g!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

-g+(+1/2)g+6-9-(+71/2)=0

We add all the numbers together, and all the variables

-1g+(+1/2)g-3-(+71/2)=0

We multiply parentheses

g^2-1g-3-(+71/2)=0

We get rid of parentheses

g^2-1g-3-71/2=0

We multiply all the terms by the denominator


g^2*2-1g*2-71-3*2=0

We add all the numbers together, and all the variables

g^2*2-1g*2-77=0

Wy multiply elements

2g^2-2g-77=0

a = 2; b = -2; c = -77;
Δ = b2-4ac
Δ = -22-4·2·(-77)
Δ = 620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{155}}{2*2}=\frac{2-2\sqrt{155}}{4}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{155}}{2*2}=\frac{2+2\sqrt{155}}{4}
$