X^2-14x=-41

Solution for X^2-14x=-41 equation:

X^2-14X=-41

We move all terms to the left:

X^2-14X-(-41)=0

We add all the numbers together, and all the variables

X^2-14X+41=0

a = 1; b = -14; c = +41;
Δ = b2-4ac
Δ = -142-4·1·41
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{2}}{2*1}=\frac{14-4\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{2}}{2*1}=\frac{14+4\sqrt{2}}{2}
$