224=x2+10x+24

Solution for 224=x2+10x+24 equation:

224=x2+10x+24

We move all terms to the left:

224-(x2+10x+24)=0

We add all the numbers together, and all the variables

-(+x^2+10x+24)+224=0

We get rid of parentheses

-x^2-10x-24+224=0

We add all the numbers together, and all the variables

-1x^2-10x+200=0

a = -1; b = -10; c = +200;
Δ = b2-4ac
Δ = -102-4·(-1)·200
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*-1}=\frac{40}{-2}
=-20
$