X^2-6x-62=-10

Solution for X^2-6x-62=-10 equation:

X^2-6X-62=-10

We move all terms to the left:

X^2-6X-62-(-10)=0

We add all the numbers together, and all the variables

X^2-6X-52=0

a = 1; b = -6; c = -52;
Δ = b2-4ac
Δ = -62-4·1·(-52)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{61}}{2*1}=\frac{6-2\sqrt{61}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{61}}{2*1}=\frac{6+2\sqrt{61}}{2}
$