5x^2-4x-81=0

Solution for 5x^2-4x-81=0 equation:

5x^2-4x-81=0

a = 5; b = -4; c = -81;
Δ = b2-4ac
Δ = -42-4·5·(-81)
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{409}}{2*5}=\frac{4-2\sqrt{409}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{409}}{2*5}=\frac{4+2\sqrt{409}}{10}
$