x^2+10x+1=24

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

x^2+10x+1=24

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2+10x-23=0

a = 1; b = 10; c = -23;
Δ = b2-4ac
Δ = 102-4·1·(-23)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8\sqrt{3}}{2*1}=\frac{-10-8\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8\sqrt{3}}{2*1}=\frac{-10+8\sqrt{3}}{2}
$