4n^2-11=-6n

Solution for 4n^2-11=-6n equation:

4n^2-11=-6n

We move all terms to the left:

4n^2-11-(-6n)=0

We get rid of parentheses

4n^2+6n-11=0

a = 4; b = 6; c = -11;
Δ = b2-4ac
Δ = 62-4·4·(-11)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{53}}{2*4}=\frac{-6-2\sqrt{53}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{53}}{2*4}=\frac{-6+2\sqrt{53}}{8}
$