5x^2-9x-1=5

Solution for 5x^2-9x-1=5 equation:

5x^2-9x-1=5

We move all terms to the left:

5x^2-9x-1-(5)=0

We add all the numbers together, and all the variables

5x^2-9x-6=0

a = 5; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·5·(-6)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{201}}{2*5}=\frac{9-\sqrt{201}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{201}}{2*5}=\frac{9+\sqrt{201}}{10}
$