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=0.125Y^2+6Y-22
We move all terms to the left:
-(0.125Y^2+6Y-22)=0
We get rid of parentheses
-0.125Y^2-6Y+22=0
a = -0.125; b = -6; c = +22;
Δ = b2-4ac
Δ = -62-4·(-0.125)·22
Δ = 47
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{-(-6)-\sqrt{47}}{2*-0.125}=\frac{6-\sqrt{47}}{-0.25} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{47}}{2*-0.125}=\frac{6+\sqrt{47}}{-0.25} $
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