x^2-39x+45=0

Solution for x^2-39x+45=0 equation:

x^2-39x+45=0

a = 1; b = -39; c = +45;
Δ = b2-4ac
Δ = -392-4·1·45
Δ = 1341
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:

$\sqrt{\Delta}=\sqrt{1341}=\sqrt{9*149}=\sqrt{9}*\sqrt{149}=3\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{149}}{2*1}=\frac{39-3\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{149}}{2*1}=\frac{39+3\sqrt{149}}{2}
$