x2+13=3x+14

Solution for x2+13=3x+14 equation:

x2+13=3x+14

We move all terms to the left:

x2+13-(3x+14)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^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}
$