x2-34;x=10

Solution for x2-34;x=10 equation:

x2-34x=10

We move all terms to the left:

x2-34x-(10)=0

We add all the numbers together, and all the variables

x^2-34x-10=0

a = 1; b = -34; c = -10;
Δ = b2-4ac
Δ = -342-4·1·(-10)
Δ = 1196
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:

$\sqrt{\Delta}=\sqrt{1196}=\sqrt{4*299}=\sqrt{4}*\sqrt{299}=2\sqrt{299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{299}}{2*1}=\frac{34-2\sqrt{299}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{299}}{2*1}=\frac{34+2\sqrt{299}}{2}
$