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(G)=1/2G+6
We move all terms to the left:
(G)-(1/2G+6)=0
Domain of the equation: 2G+6)!=0We get rid of parentheses
G∈R
G-1/2G-6=0
We multiply all the terms by the denominator
G*2G-6*2G-1=0
Wy multiply elements
2G^2-12G-1=0
a = 2; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·2·(-1)
Δ = 152
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}$$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{38}}{2*2}=\frac{12-2\sqrt{38}}{4} $$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{38}}{2*2}=\frac{12+2\sqrt{38}}{4} $
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