x^2-10x=38

Solution for x^2-10x=38 equation:

x^2-10x=38

We move all terms to the left:

x^2-10x-(38)=0

a = 1; b = -10; c = -38;
Δ = b2-4ac
Δ = -102-4·1·(-38)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{7}}{2*1}=\frac{10-6\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{7}}{2*1}=\frac{10+6\sqrt{7}}{2}
$