5x^2+4x^-1=1

Solution for 5x^2+4x^-1=1 equation:

5x^2+4x^-1=1

We move all terms to the left:

5x^2+4x^-1-(1)=0

We add all the numbers together, and all the variables

5x^2+4x-2=0

a = 5; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·5·(-2)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{14}}{2*5}=\frac{-4-2\sqrt{14}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{14}}{2*5}=\frac{-4+2\sqrt{14}}{10}
$