X^2-38x+140=0

Solution for X^2-38x+140=0 equation:

X^2-38X+140=0

a = 1; b = -38; c = +140;
Δ = b2-4ac
Δ = -382-4·1·140
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{221}}{2*1}=\frac{38-2\sqrt{221}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{221}}{2*1}=\frac{38+2\sqrt{221}}{2}
$