13x+14=x^2

Solution for 13x+14=x^2 equation:

13x+14=x^2

We move all terms to the left:

13x+14-(x^2)=0

determiningTheFunctionDomain
-x^2+13x+14=0

We add all the numbers together, and all the variables

-1x^2+13x+14=0

a = -1; b = 13; c = +14;
Δ = b2-4ac
Δ = 132-4·(-1)·14
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-15}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+15}{2*-1}=\frac{2}{-2}
=-1
$