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=9Y-6/7Y+3
We move all terms to the left:
-(9Y-6/7Y+3)=0
Domain of the equation: 7Y+3)!=0We get rid of parentheses
Y∈R
-9Y+6/7Y-3=0
We multiply all the terms by the denominator
-9Y*7Y-3*7Y+6=0
Wy multiply elements
-63Y^2-21Y+6=0
a = -63; b = -21; c = +6;
Δ = b2-4ac
Δ = -212-4·(-63)·6
Δ = 1953
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{217}}{2*-63}=\frac{21-3\sqrt{217}}{-126} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{217}}{2*-63}=\frac{21+3\sqrt{217}}{-126} $
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