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96x-16x^2=40
We move all terms to the left:
96x-16x^2-(40)=0
a = -16; b = 96; c = -40;
Δ = b2-4ac
Δ = 962-4·(-16)·(-40)
Δ = 6656
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6656}=\sqrt{256*26}=\sqrt{256}*\sqrt{26}=16\sqrt{26}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-16\sqrt{26}}{2*-16}=\frac{-96-16\sqrt{26}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+16\sqrt{26}}{2*-16}=\frac{-96+16\sqrt{26}}{-32} $
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