294=x^2+7x

Solution for 294=x^2+7x equation:

294=x^2+7x

We move all terms to the left:

294-(x^2+7x)=0

We get rid of parentheses

-x^2-7x+294=0

We add all the numbers together, and all the variables

-1x^2-7x+294=0

a = -1; b = -7; c = +294;
Δ = b2-4ac
Δ = -72-4·(-1)·294
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-35}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+35}{2*-1}=\frac{42}{-2}
=-21
$