x2+34x=34

Solution for x2+34x=34 equation:

x2+34x=34

We move all terms to the left:

x2+34x-(34)=0

We add all the numbers together, and all the variables

x^2+34x-34=0

a = 1; b = 34; c = -34;
Δ = b2-4ac
Δ = 342-4·1·(-34)
Δ = 1292
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:

$\sqrt{\Delta}=\sqrt{1292}=\sqrt{4*323}=\sqrt{4}*\sqrt{323}=2\sqrt{323}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{323}}{2*1}=\frac{-34-2\sqrt{323}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{323}}{2*1}=\frac{-34+2\sqrt{323}}{2}
$