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64x^2-48x=183
We move all terms to the left:
64x^2-48x-(183)=0
a = 64; b = -48; c = -183;
Δ = b2-4ac
Δ = -482-4·64·(-183)
Δ = 49152
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{49152}=\sqrt{16384*3}=\sqrt{16384}*\sqrt{3}=128\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-128\sqrt{3}}{2*64}=\frac{48-128\sqrt{3}}{128} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+128\sqrt{3}}{2*64}=\frac{48+128\sqrt{3}}{128} $
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