x^2-10x-57=9

Solution for x^2-10x-57=9 equation:

x^2-10x-57=9

We move all terms to the left:

x^2-10x-57-(9)=0

We add all the numbers together, and all the variables

x^2-10x-66=0

a = 1; b = -10; c = -66;
Δ = b2-4ac
Δ = -102-4·1·(-66)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{91}}{2*1}=\frac{10-2\sqrt{91}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{91}}{2*1}=\frac{10+2\sqrt{91}}{2}
$