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-2.7x^2+30x+6.5=75
We move all terms to the left:
-2.7x^2+30x+6.5-(75)=0
We add all the numbers together, and all the variables
-2.7x^2+30x-68.5=0
a = -2.7; b = 30; c = -68.5;
Δ = b2-4ac
Δ = 302-4·(-2.7)·(-68.5)
Δ = 160.2
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{160.2}}{2*-2.7}=\frac{-30-\sqrt{160.2}}{-5.4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+\sqrt{160.2}}{2*-2.7}=\frac{-30+\sqrt{160.2}}{-5.4} $
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