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X2-40X-140=0
We add all the numbers together, and all the variables
X^2-40X-140=0
a = 1; b = -40; c = -140;
Δ = b2-4ac
Δ = -402-4·1·(-140)
Δ = 2160
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{15}}{2*1}=\frac{40-12\sqrt{15}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{15}}{2*1}=\frac{40+12\sqrt{15}}{2} $
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