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-2.7x^2+30x+6.5=16
We move all terms to the left:
-2.7x^2+30x+6.5-(16)=0
We add all the numbers together, and all the variables
-2.7x^2+30x-9.5=0
a = -2.7; b = 30; c = -9.5;
Δ = b2-4ac
Δ = 302-4·(-2.7)·(-9.5)
Δ = 797.4
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{797.4}}{2*-2.7}=\frac{-30-\sqrt{797.4}}{-5.4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+\sqrt{797.4}}{2*-2.7}=\frac{-30+\sqrt{797.4}}{-5.4} $
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