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

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

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

We move all terms to the left:

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


Domain of the equation: g-(-4(g+1))!=0

g∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-1g*g-(-4(g+1))+2(3=0


We calculate terms in parentheses: -(-4(g+1)), so:

-4(g+1)

We multiply parentheses

-4g-4

Back to the equation:

-(-4g-4)


We add all the numbers together, and all the variables

-1g*g-(-4g-4)=0

Wy multiply elements

-1g^2-(-4g-4)=0

We get rid of parentheses

-1g^2+4g+4=0

a = -1; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-1)·4
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-1}=\frac{-4-4\sqrt{2}}{-2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-1}=\frac{-4+4\sqrt{2}}{-2}
$