0=x2+9x-234

Solution for 0=x2+9x-234 equation:

0=x2+9x-234

We move all terms to the left:

0-(x2+9x-234)=0

We add all the numbers together, and all the variables

-(+x^2+9x-234)+0=0

We add all the numbers together, and all the variables

-(+x^2+9x-234)=0

We get rid of parentheses

-x^2-9x+234=0

We add all the numbers together, and all the variables

-1x^2-9x+234=0

a = -1; b = -9; c = +234;
Δ = b2-4ac
Δ = -92-4·(-1)·234
Δ = 1017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{113}}{2*-1}=\frac{9-3\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{113}}{2*-1}=\frac{9+3\sqrt{113}}{-2}
$