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3/4g-9=8g
We move all terms to the left:
3/4g-9-(8g)=0
Domain of the equation: 4g!=0We add all the numbers together, and all the variables
g!=0/4
g!=0
g∈R
-8g+3/4g-9=0
We multiply all the terms by the denominator
-8g*4g-9*4g+3=0
Wy multiply elements
-32g^2-36g+3=0
a = -32; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·(-32)·3
Δ = 1680
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}$$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{105}}{2*-32}=\frac{36-4\sqrt{105}}{-64} $$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{105}}{2*-32}=\frac{36+4\sqrt{105}}{-64} $
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