X^2-34x+81=0

Solution for X^2-34x+81=0 equation:

X^2-34X+81=0

a = 1; b = -34; c = +81;
Δ = b2-4ac
Δ = -342-4·1·81
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-8\sqrt{13}}{2*1}=\frac{34-8\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+8\sqrt{13}}{2*1}=\frac{34+8\sqrt{13}}{2}
$