x^2-14x-40=-5

Solution for x^2-14x-40=-5 equation:

x^2-14x-40=-5

We move all terms to the left:

x^2-14x-40-(-5)=0

We add all the numbers together, and all the variables

x^2-14x-35=0

a = 1; b = -14; c = -35;
Δ = b2-4ac
Δ = -142-4·1·(-35)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{21}}{2*1}=\frac{14-4\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{21}}{2*1}=\frac{14+4\sqrt{21}}{2}
$