X^2-10x+10=35

Solution for X^2-10x+10=35 equation:

X^2-10X+10=35

We move all terms to the left:

X^2-10X+10-(35)=0

We add all the numbers together, and all the variables

X^2-10X-25=0

a = 1; b = -10; c = -25;
Δ = b2-4ac
Δ = -102-4·1·(-25)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{2}}{2*1}=\frac{10-10\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{2}}{2*1}=\frac{10+10\sqrt{2}}{2}
$