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4g+4g(-7+4g)=1-g
We move all terms to the left:
4g+4g(-7+4g)-(1-g)=0
We add all the numbers together, and all the variables
4g+4g(4g-7)-(-1g+1)=0
We multiply parentheses
16g^2+4g-28g-(-1g+1)=0
We get rid of parentheses
16g^2+4g-28g+1g-1=0
We add all the numbers together, and all the variables
16g^2-23g-1=0
a = 16; b = -23; c = -1;
Δ = b2-4ac
Δ = -232-4·16·(-1)
Δ = 593
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}$$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{593}}{2*16}=\frac{23-\sqrt{593}}{32} $$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{593}}{2*16}=\frac{23+\sqrt{593}}{32} $
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