x2-14x+40=2x+1

Solution for x2-14x+40=2x+1 equation:

x2-14x+40=2x+1

We move all terms to the left:

x2-14x+40-(2x+1)=0

We add all the numbers together, and all the variables

x^2-14x-(2x+1)+40=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+39=0

a = 1; b = -16; c = +39;
Δ = b2-4ac
Δ = -162-4·1·39
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-10}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10}{2*1}=\frac{26}{2}
=13
$