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1/2g-4=2g-1/2g=4
We move all terms to the left:
1/2g-4-(2g-1/2g)=0
Domain of the equation: 2g!=0
g!=0/2
g!=0
g∈R
Domain of the equation: 2g)!=0We add all the numbers together, and all the variables
g!=0/1
g!=0
g∈R
1/2g-(+2g-1/2g)-4=0
We get rid of parentheses
1/2g-2g+1/2g-4=0
We multiply all the terms by the denominator
-2g*2g-4*2g+1+1=0
We add all the numbers together, and all the variables
-2g*2g-4*2g+2=0
Wy multiply elements
-4g^2-8g+2=0
a = -4; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·(-4)·2
Δ = 96
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}$$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*-4}=\frac{8-4\sqrt{6}}{-8} $$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*-4}=\frac{8+4\sqrt{6}}{-8} $
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