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-16x^2+91x+4=84
We move all terms to the left:
-16x^2+91x+4-(84)=0
We add all the numbers together, and all the variables
-16x^2+91x-80=0
a = -16; b = 91; c = -80;
Δ = b2-4ac
Δ = 912-4·(-16)·(-80)
Δ = 3161
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{-(91)-\sqrt{3161}}{2*-16}=\frac{-91-\sqrt{3161}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{3161}}{2*-16}=\frac{-91+\sqrt{3161}}{-32} $
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