1=x^2+10x+24

Solution for 1=x^2+10x+24 equation:

1=x^2+10x+24

We move all terms to the left:

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

We get rid of parentheses

-x^2-10x-24+1=0

We add all the numbers together, and all the variables

-1x^2-10x-23=0

a = -1; b = -10; c = -23;
Δ = b2-4ac
Δ = -102-4·(-1)·(-23)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{2}}{2*-1}=\frac{10-2\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{2}}{2*-1}=\frac{10+2\sqrt{2}}{-2}
$