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7x^2-62x-9=0
a = 7; b = -62; c = -9;
Δ = b2-4ac
Δ = -622-4·7·(-9)
Δ = 4096
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{4096}=64$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-64}{2*7}=\frac{-2}{14} =-1/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+64}{2*7}=\frac{126}{14} =9 $
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