x^2-38x+49=0

Solution for x^2-38x+49=0 equation:

x^2-38x+49=0

a = 1; b = -38; c = +49;
Δ = b2-4ac
Δ = -382-4·1·49
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-4\sqrt{78}}{2*1}=\frac{38-4\sqrt{78}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+4\sqrt{78}}{2*1}=\frac{38+4\sqrt{78}}{2}
$