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0=197-21x-16x^2
We move all terms to the left:
0-(197-21x-16x^2)=0
We add all the numbers together, and all the variables
-(197-21x-16x^2)=0
We get rid of parentheses
16x^2+21x-197=0
a = 16; b = 21; c = -197;
Δ = b2-4ac
Δ = 212-4·16·(-197)
Δ = 13049
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{-(21)-\sqrt{13049}}{2*16}=\frac{-21-\sqrt{13049}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{13049}}{2*16}=\frac{-21+\sqrt{13049}}{32} $
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