0=x^2+8x+3x+24-234

Solution for 0=x^2+8x+3x+24-234 equation:

0=x^2+8x+3x+24-234

We move all terms to the left:

0-(x^2+8x+3x+24-234)=0

We add all the numbers together, and all the variables

-(x^2+8x+3x+24-234)=0

We get rid of parentheses

-x^2-8x-3x-24+234=0

We add all the numbers together, and all the variables

-1x^2-11x+210=0

a = -1; b = -11; c = +210;
Δ = b2-4ac
Δ = -112-4·(-1)·210
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*-1}=\frac{42}{-2}
=-21
$