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2x^2-138x-2160=0
a = 2; b = -138; c = -2160;
Δ = b2-4ac
Δ = -1382-4·2·(-2160)
Δ = 36324
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36324}=\sqrt{36*1009}=\sqrt{36}*\sqrt{1009}=6\sqrt{1009}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-6\sqrt{1009}}{2*2}=\frac{138-6\sqrt{1009}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+6\sqrt{1009}}{2*2}=\frac{138+6\sqrt{1009}}{4} $
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