5x^2-10x-1=-4

Solution for 5x^2-10x-1=-4 equation:

5x^2-10x-1=-4

We move all terms to the left:

5x^2-10x-1-(-4)=0

We add all the numbers together, and all the variables

5x^2-10x+3=0

a = 5; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·5·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{10}}{2*5}=\frac{10-2\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{10}}{2*5}=\frac{10+2\sqrt{10}}{10}
$