-36n^2+1=076n-128

Solution for -36n^2+1=076n-128 equation:

-36n^2+1=076n-128

We move all terms to the left:

-36n^2+1-(076n-128)=0

We get rid of parentheses

-36n^2-076n+128+1=0

We add all the numbers together, and all the variables

-36n^2-76n+129=0

a = -36; b = -76; c = +129;
Δ = b2-4ac
Δ = -762-4·(-36)·129
Δ = 24352
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:

$\sqrt{\Delta}=\sqrt{24352}=\sqrt{16*1522}=\sqrt{16}*\sqrt{1522}=4\sqrt{1522}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{1522}}{2*-36}=\frac{76-4\sqrt{1522}}{-72}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{1522}}{2*-36}=\frac{76+4\sqrt{1522}}{-72}
$