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10x^2+182x-85=0
a = 10; b = 182; c = -85;
Δ = b2-4ac
Δ = 1822-4·10·(-85)
Δ = 36524
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36524}=\sqrt{4*9131}=\sqrt{4}*\sqrt{9131}=2\sqrt{9131}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(182)-2\sqrt{9131}}{2*10}=\frac{-182-2\sqrt{9131}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(182)+2\sqrt{9131}}{2*10}=\frac{-182+2\sqrt{9131}}{20} $
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