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-16x^2+64x=36
We move all terms to the left:
-16x^2+64x-(36)=0
a = -16; b = 64; c = -36;
Δ = b2-4ac
Δ = 642-4·(-16)·(-36)
Δ = 1792
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-16\sqrt{7}}{2*-16}=\frac{-64-16\sqrt{7}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+16\sqrt{7}}{2*-16}=\frac{-64+16\sqrt{7}}{-32} $
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