X^2-68x+333=0

Solution for X^2-68x+333=0 equation:

X^2-68X+333=0

a = 1; b = -68; c = +333;
Δ = b2-4ac
Δ = -682-4·1·333
Δ = 3292
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:

$\sqrt{\Delta}=\sqrt{3292}=\sqrt{4*823}=\sqrt{4}*\sqrt{823}=2\sqrt{823}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-2\sqrt{823}}{2*1}=\frac{68-2\sqrt{823}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+2\sqrt{823}}{2*1}=\frac{68+2\sqrt{823}}{2}
$