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5.5=-2.7x^2+30x
We move all terms to the left:
5.5-(-2.7x^2+30x)=0
We get rid of parentheses
2.7x^2-30x+5.5=0
a = 2.7; b = -30; c = +5.5;
Δ = b2-4ac
Δ = -302-4·2.7·5.5
Δ = 840.6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-\sqrt{840.6}}{2*2.7}=\frac{30-\sqrt{840.6}}{5.4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{840.6}}{2*2.7}=\frac{30+\sqrt{840.6}}{5.4} $
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