n2-2n-43=-10

Solution for n2-2n-43=-10 equation:

n2-2n-43=-10

We move all terms to the left:

n2-2n-43-(-10)=0

We add all the numbers together, and all the variables

n^2-2n-33=0

a = 1; b = -2; c = -33;
Δ = b2-4ac
Δ = -22-4·1·(-33)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{34}}{2*1}=\frac{2-2\sqrt{34}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{34}}{2*1}=\frac{2+2\sqrt{34}}{2}
$