x^2-14x-105=-10

Solution for x^2-14x-105=-10 equation:

x^2-14x-105=-10

We move all terms to the left:

x^2-14x-105-(-10)=0

We add all the numbers together, and all the variables

x^2-14x-95=0

a = 1; b = -14; c = -95;
Δ = b2-4ac
Δ = -142-4·1·(-95)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-24}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+24}{2*1}=\frac{38}{2}
=19
$