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=9Y^2+5Y-8
We move all terms to the left:
-(9Y^2+5Y-8)=0
We get rid of parentheses
-9Y^2-5Y+8=0
a = -9; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·(-9)·8
Δ = 313
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{313}}{2*-9}=\frac{5-\sqrt{313}}{-18} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{313}}{2*-9}=\frac{5+\sqrt{313}}{-18} $
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