x2-20x=-34

Solution for x2-20x=-34 equation:

x2-20x=-34

We move all terms to the left:

x2-20x-(-34)=0

We add all the numbers together, and all the variables

x^2-20x+34=0

a = 1; b = -20; c = +34;
Δ = b2-4ac
Δ = -202-4·1·34
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{66}}{2*1}=\frac{20-2\sqrt{66}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{66}}{2*1}=\frac{20+2\sqrt{66}}{2}
$