5a^2-2a-47=0

Solution for 5a^2-2a-47=0 equation:

5a^2-2a-47=0

a = 5; b = -2; c = -47;
Δ = b2-4ac
Δ = -22-4·5·(-47)
Δ = 944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{59}}{2*5}=\frac{2-4\sqrt{59}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{59}}{2*5}=\frac{2+4\sqrt{59}}{10}
$