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209=16x^2-9x-15
We move all terms to the left:
209-(16x^2-9x-15)=0
We get rid of parentheses
-16x^2+9x+15+209=0
We add all the numbers together, and all the variables
-16x^2+9x+224=0
a = -16; b = 9; c = +224;
Δ = b2-4ac
Δ = 92-4·(-16)·224
Δ = 14417
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{-(9)-\sqrt{14417}}{2*-16}=\frac{-9-\sqrt{14417}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{14417}}{2*-16}=\frac{-9+\sqrt{14417}}{-32} $
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