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7x^2-34x-5=0
a = 7; b = -34; c = -5;
Δ = b2-4ac
Δ = -342-4·7·(-5)
Δ = 1296
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1296}=36$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-36}{2*7}=\frac{-2}{14} =-1/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+36}{2*7}=\frac{70}{14} =5 $
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