X^2+38x+45=0

Solution for X^2+38x+45=0 equation:

X^2+38X+45=0

a = 1; b = 38; c = +45;
Δ = b2-4ac
Δ = 382-4·1·45
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-4\sqrt{79}}{2*1}=\frac{-38-4\sqrt{79}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+4\sqrt{79}}{2*1}=\frac{-38+4\sqrt{79}}{2}
$