X^2-28x+74=0

Solution for X^2-28x+74=0 equation:

X^2-28X+74=0

a = 1; b = -28; c = +74;
Δ = b2-4ac
Δ = -282-4·1·74
Δ = 488
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:

$\sqrt{\Delta}=\sqrt{488}=\sqrt{4*122}=\sqrt{4}*\sqrt{122}=2\sqrt{122}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{122}}{2*1}=\frac{28-2\sqrt{122}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{122}}{2*1}=\frac{28+2\sqrt{122}}{2}
$