814=x^2+3x+4

Solution for 814=x^2+3x+4 equation:

814=x^2+3x+4

We move all terms to the left:

814-(x^2+3x+4)=0

We get rid of parentheses

-x^2-3x-4+814=0

We add all the numbers together, and all the variables

-1x^2-3x+810=0

a = -1; b = -3; c = +810;
Δ = b2-4ac
Δ = -32-4·(-1)·810
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-57}{2*-1}=\frac{-54}{-2}
=+27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+57}{2*-1}=\frac{60}{-2}
=-30
$