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16x=30000-9x^2
We move all terms to the left:
16x-(30000-9x^2)=0
We get rid of parentheses
9x^2+16x-30000=0
a = 9; b = 16; c = -30000;
Δ = b2-4ac
Δ = 162-4·9·(-30000)
Δ = 1080256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1080256}=\sqrt{64*16879}=\sqrt{64}*\sqrt{16879}=8\sqrt{16879}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{16879}}{2*9}=\frac{-16-8\sqrt{16879}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{16879}}{2*9}=\frac{-16+8\sqrt{16879}}{18} $
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