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(G)=0.5(G-3/4)2
We move all terms to the left:
(G)-(0.5(G-3/4)2)=0
We add all the numbers together, and all the variables
G-(0.5(+G-3/4)2)=0
We multiply all the terms by the denominator
G*4)2)-(0.5(+G-3=0
We add all the numbers together, and all the variables
G+G*4)2)-(0.5(-3=0
Wy multiply elements
4G^2+G-3=0
a = 4; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·4·(-3)
Δ = 49
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{49}=7$$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*4}=\frac{-8}{8} =-1 $$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*4}=\frac{6}{8} =3/4 $
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