0=-16x^2+78x+5

Solution for 0=-16x^2+78x+5 equation:

0=-16x^2+78x+5

We move all terms to the left:

0-(-16x^2+78x+5)=0

We add all the numbers together, and all the variables

-(-16x^2+78x+5)=0

We get rid of parentheses

16x^2-78x-5=0

a = 16; b = -78; c = -5;
Δ = b2-4ac
Δ = -782-4·16·(-5)
Δ = 6404
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:

$\sqrt{\Delta}=\sqrt{6404}=\sqrt{4*1601}=\sqrt{4}*\sqrt{1601}=2\sqrt{1601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1601}}{2*16}=\frac{78-2\sqrt{1601}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1601}}{2*16}=\frac{78+2\sqrt{1601}}{32}
$