-11n^2+4n=-7+2n

Solution for -11n^2+4n=-7+2n equation:

-11n^2+4n=-7+2n

We move all terms to the left:

-11n^2+4n-(-7+2n)=0

We add all the numbers together, and all the variables

-11n^2+4n-(2n-7)=0

We get rid of parentheses

-11n^2+4n-2n+7=0

We add all the numbers together, and all the variables

-11n^2+2n+7=0

a = -11; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-11)·7
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{78}}{2*-11}=\frac{-2-2\sqrt{78}}{-22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{78}}{2*-11}=\frac{-2+2\sqrt{78}}{-22}
$