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3000=32x^2
We move all terms to the left:
3000-(32x^2)=0
a = -32; b = 0; c = +3000;
Δ = b2-4ac
Δ = 02-4·(-32)·3000
Δ = 384000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{384000}=\sqrt{25600*15}=\sqrt{25600}*\sqrt{15}=160\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{15}}{2*-32}=\frac{0-160\sqrt{15}}{-64} =-\frac{160\sqrt{15}}{-64} =-\frac{5\sqrt{15}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{15}}{2*-32}=\frac{0+160\sqrt{15}}{-64} =\frac{160\sqrt{15}}{-64} =\frac{5\sqrt{15}}{-2} $
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