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10x^2+4x-5x-102=0
We add all the numbers together, and all the variables
10x^2-1x-102=0
a = 10; b = -1; c = -102;
Δ = b2-4ac
Δ = -12-4·10·(-102)
Δ = 4081
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{4081}}{2*10}=\frac{1-\sqrt{4081}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{4081}}{2*10}=\frac{1+\sqrt{4081}}{20} $
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