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115x^2-180x-6500=0
a = 115; b = -180; c = -6500;
Δ = b2-4ac
Δ = -1802-4·115·(-6500)
Δ = 3022400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3022400}=\sqrt{1600*1889}=\sqrt{1600}*\sqrt{1889}=40\sqrt{1889}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-40\sqrt{1889}}{2*115}=\frac{180-40\sqrt{1889}}{230} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+40\sqrt{1889}}{2*115}=\frac{180+40\sqrt{1889}}{230} $
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