x^2+24x+67=9

Solution for x^2+24x+67=9 equation:

x^2+24x+67=9

We move all terms to the left:

x^2+24x+67-(9)=0

We add all the numbers together, and all the variables

x^2+24x+58=0

a = 1; b = 24; c = +58;
Δ = b2-4ac
Δ = 242-4·1·58
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{86}}{2*1}=\frac{-24-2\sqrt{86}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{86}}{2*1}=\frac{-24+2\sqrt{86}}{2}
$