3x+14=x^2+13

Solution for 3x+14=x^2+13 equation:

3x+14=x^2+13

We move all terms to the left:

3x+14-(x^2+13)=0

We get rid of parentheses

-x^2+3x-13+14=0

We add all the numbers together, and all the variables

-1x^2+3x+1=0

a = -1; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-1)·1
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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