7q^2-5q-1=0

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Solution for 7q^2-5q-1=0 equation: 



7q^2-5q-1=0

a = 7; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·7·(-1)
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{53}}{2*7}=\frac{5-\sqrt{53}}{14}
$


$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*7}=\frac{5+\sqrt{53}}{14}
$

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