2x^2-10x-1=20

Solution for 2x^2-10x-1=20 equation:

2x^2-10x-1=20

We move all terms to the left:

2x^2-10x-1-(20)=0

We add all the numbers together, and all the variables

2x^2-10x-21=0

a = 2; b = -10; c = -21;
Δ = b2-4ac
Δ = -102-4·2·(-21)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{67}}{2*2}=\frac{10-2\sqrt{67}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{67}}{2*2}=\frac{10+2\sqrt{67}}{4}
$