22g(g-1)=2g+8

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Solution for 22g(g-1)=2g+8 equation:



22g(g-1)=2g+8
We move all terms to the left:
22g(g-1)-(2g+8)=0
We multiply parentheses
22g^2-22g-(2g+8)=0
We get rid of parentheses
22g^2-22g-2g-8=0
We add all the numbers together, and all the variables
22g^2-24g-8=0
a = 22; b = -24; c = -8;
Δ = b2-4ac
Δ = -242-4·22·(-8)
Δ = 1280
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:
$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{5}}{2*22}=\frac{24-16\sqrt{5}}{44} $
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{5}}{2*22}=\frac{24+16\sqrt{5}}{44} $

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