5x^2-14x-71=0

Solution for 5x^2-14x-71=0 equation:

5x^2-14x-71=0

a = 5; b = -14; c = -71;
Δ = b2-4ac
Δ = -142-4·5·(-71)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{101}}{2*5}=\frac{14-4\sqrt{101}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{101}}{2*5}=\frac{14+4\sqrt{101}}{10}
$