x^2-14x+49=85

Solution for x^2-14x+49=85 equation:

x^2-14x+49=85

We move all terms to the left:

x^2-14x+49-(85)=0

We add all the numbers together, and all the variables

x^2-14x-36=0

a = 1; b = -14; c = -36;
Δ = b2-4ac
Δ = -142-4·1·(-36)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{85}}{2*1}=\frac{14-2\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{85}}{2*1}=\frac{14+2\sqrt{85}}{2}
$