x^2-14x-40=2x+1

Solution for x^2-14x-40=2x+1 equation:

x^2-14x-40=2x+1

We move all terms to the left:

x^2-14x-40-(2x+1)=0

We get rid of parentheses

x^2-14x-2x-1-40=0

We add all the numbers together, and all the variables

x^2-16x-41=0

a = 1; b = -16; c = -41;
Δ = b2-4ac
Δ = -162-4·1·(-41)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{105}}{2*1}=\frac{16-2\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{105}}{2*1}=\frac{16+2\sqrt{105}}{2}
$