6x-1=x^2-8x-20

Solution for 6x-1=x^2-8x-20 equation:

6x-1=x^2-8x-20

We move all terms to the left:

6x-1-(x^2-8x-20)=0

We get rid of parentheses

-x^2+6x+8x+20-1=0

We add all the numbers together, and all the variables

-1x^2+14x+19=0

a = -1; b = 14; c = +19;
Δ = b2-4ac
Δ = 142-4·(-1)·19
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{17}}{2*-1}=\frac{-14-4\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{17}}{2*-1}=\frac{-14+4\sqrt{17}}{-2}
$