1116=4x^2-73x+1296

Solution for 1116=4x^2-73x+1296 equation:

1116=4x^2-73x+1296

We move all terms to the left:

1116-(4x^2-73x+1296)=0

We get rid of parentheses

-4x^2+73x-1296+1116=0

We add all the numbers together, and all the variables

-4x^2+73x-180=0

a = -4; b = 73; c = -180;
Δ = b2-4ac
Δ = 732-4·(-4)·(-180)
Δ = 2449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(73)-\sqrt{2449}}{2*-4}=\frac{-73-\sqrt{2449}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(73)+\sqrt{2449}}{2*-4}=\frac{-73+\sqrt{2449}}{-8}
$