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8x-138x^2+102=0
a = -138; b = 8; c = +102;
Δ = b2-4ac
Δ = 82-4·(-138)·102
Δ = 56368
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56368}=\sqrt{16*3523}=\sqrt{16}*\sqrt{3523}=4\sqrt{3523}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{3523}}{2*-138}=\frac{-8-4\sqrt{3523}}{-276} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{3523}}{2*-138}=\frac{-8+4\sqrt{3523}}{-276} $
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