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8x^2+54x-85=0
a = 8; b = 54; c = -85;
Δ = b2-4ac
Δ = 542-4·8·(-85)
Δ = 5636
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5636}=\sqrt{4*1409}=\sqrt{4}*\sqrt{1409}=2\sqrt{1409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{1409}}{2*8}=\frac{-54-2\sqrt{1409}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{1409}}{2*8}=\frac{-54+2\sqrt{1409}}{16} $
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