x^2+34x+273=800

Solution for x^2+34x+273=800 equation:

x^2+34x+273=800

We move all terms to the left:

x^2+34x+273-(800)=0

We add all the numbers together, and all the variables

x^2+34x-527=0

a = 1; b = 34; c = -527;
Δ = b2-4ac
Δ = 342-4·1·(-527)
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-8\sqrt{51}}{2*1}=\frac{-34-8\sqrt{51}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+8\sqrt{51}}{2*1}=\frac{-34+8\sqrt{51}}{2}
$