X2-10x-65=-10

Solution for X2-10x-65=-10 equation:

X2-10X-65=-10

We move all terms to the left:

X2-10X-65-(-10)=0

We add all the numbers together, and all the variables

X^2-10X-55=0

a = 1; b = -10; c = -55;
Δ = b2-4ac
Δ = -102-4·1·(-55)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{5}}{2*1}=\frac{10-8\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{5}}{2*1}=\frac{10+8\sqrt{5}}{2}
$