X^2-35x+205=0

Solution for X^2-35x+205=0 equation:

X^2-35X+205=0

a = 1; b = -35; c = +205;
Δ = b2-4ac
Δ = -352-4·1·205
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-9\sqrt{5}}{2*1}=\frac{35-9\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+9\sqrt{5}}{2*1}=\frac{35+9\sqrt{5}}{2}
$