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31x^2-118x-180=0
a = 31; b = -118; c = -180;
Δ = b2-4ac
Δ = -1182-4·31·(-180)
Δ = 36244
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36244}=\sqrt{4*9061}=\sqrt{4}*\sqrt{9061}=2\sqrt{9061}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-2\sqrt{9061}}{2*31}=\frac{118-2\sqrt{9061}}{62} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+2\sqrt{9061}}{2*31}=\frac{118+2\sqrt{9061}}{62} $
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