x^2+10x+24=224

Solution for x^2+10x+24=224 equation:

x^2+10x+24=224

We move all terms to the left:

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

We add all the numbers together, and all the variables

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