10-14x-x^2=0

Solution for 10-14x-x^2=0 equation:

10-14x-x^2=0

We add all the numbers together, and all the variables

-1x^2-14x+10=0

a = -1; b = -14; c = +10;
Δ = b2-4ac
Δ = -142-4·(-1)·10
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{59}}{2*-1}=\frac{14-2\sqrt{59}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{59}}{2*-1}=\frac{14+2\sqrt{59}}{-2}
$