-16x^2+144x+20=1

Solution for -16x^2+144x+20=1 equation:

-16x^2+144x+20=1

We move all terms to the left:

-16x^2+144x+20-(1)=0

We add all the numbers together, and all the variables

-16x^2+144x+19=0

a = -16; b = 144; c = +19;
Δ = b2-4ac
Δ = 1442-4·(-16)·19
Δ = 21952
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{21952}=\sqrt{3136*7}=\sqrt{3136}*\sqrt{7}=56\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-56\sqrt{7}}{2*-16}=\frac{-144-56\sqrt{7}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+56\sqrt{7}}{2*-16}=\frac{-144+56\sqrt{7}}{-32}
$